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A SYSTEM 



OF 



NATURAL PHILOSOPHY, 

DESIGNED FOR 

I 

THE USE OF SCHOOLS AND ACADEMIES, 

ON THE BASIS OF 

THE BOOK OF SCIENCE BY MR. J. M. MOFFAT. 

COMPRISING 

MECHANICS, I PYRONOMICS, 

HYDROSTATICS, gJTr^TrTTY 

HYDRAULICS, E^ECTRICIT \, 

PNEUMATICS, ? A ^ A J^,' 

ACOUSTICS, I MAGNETISM, 



WITH EMENDATIONS, NOTES, QUESTIONS FOR EXAMINATION, LISTS 

OF WORDS FOR REFERENCE, SOME ADDITIONAL 

ILLUSTRATIONS, AND AN INDEX. 

BY WALTER R. JOHNSON, A.M. 

Professor of Chemistry in the Pennsylvania College, Philadelphia, and late 

Professor of Mechanics and Natural Philosophy in the Franklin 

Institute of the State of Pennsylvania, &c. &c. 



ILLUSTRATED BY 
MORE THAN TWO HUNDRED ENGRAVINGS. 



EIGHTH EDITION. 



PHILADELPHIA: 
PUBLISHED BY EDWARD C.B1DDLE, 

No. 6 SOUTH FIFTH STREET. 

1845. 



Entered according to Act of Congress, in the year 1836, by 

Key & Bjddle, 
:h« Clerk's Office of the District Court of the Eastern District of 
Pennsylvania. 



/ 



g% ^ 



& 



CONTENTS. 



Preface. 
Lxtrodttctiox, 9. 



MECHANICS. 



Preliminary Observations, 17 — Mobility, 18 — Elasticity, 23 — Velo- 
city of Motion, 25 — Different Kinds of Motion, 27 — Parallelogram of 
Forces, 31 — Gravitation, 36 — Accelerated Motion, 47 — Curvilinear Mo- 
tion, 53 — Oscillation of tbe Pendulum, 59 — Centre of Gravity, 65 — 
Mecbanic Powers, 72 — Lever, 74 — Wheel and Axle, 83 — Machine of 
Oblique Action, 87— Pulley, 89— Inclined Plane, 91— Wedge, 93— 
Screw, 94 — Compound Machinery, 98 — Friction, 108 — Rigidity of Cor- 
dage, 111 — Strength of Materials, 112 — Moving Powers, 113 — Works 
on Mechanics, 121. 

HYDROSTATICS. 

Preliminary Remarks, 122 — Properties of Liquids, 123 — Hydrostatic 
Pressure, 129 — Specific Gravity, 147 — Capillary Attraction, 162 — 
Works on Hydrostatics, 165 — Hydraulics, 166 — Hydraulic Machines, 
172 — Works on Hydraulics, 179. 

PNEUMATICS. 

General Observations, 179 — Common Properties of aerial Fluids, 181 
—Different Kinds of Airs, 183— Elasticity of Air, 185— Weight of 
Air, 196 — Pneumatic Instruments and Experiments, 199 — Aerosta- 
tics, 218— Air-balloon, 221— Parachute, 223— Paper-kite, 226— Diving- 
bell, 227— Torpedo, 230— Works on Pneumatics, 230. 

ACOUSTICS 

Cause of Sound, 231 — Sonorous Vibrations, 233 — Velocity of Sound, 
238 — Musical Sounds, 242 — Musical Scale, 246 — Musical Instruments, 
254 — Human Voice, 262— Reflection of Sound, 266— Echoes, 267— 
Ventriloquism, 273 — Works on Acoustics, 276. 



4 CONTENTS. 

PYRONOMICS. 

Causes of Heat and Cold, 277— Sources of Heat, 280— Effects of 
Heat, 288 — Instruments for measuring Temperature, 292 — Latent Heat, 
303— Ebullition, 309— Steam-engine, 313— Propagation of Heat, 320 
-Caloric Engine, 323— Works on Heat, 332. 

OPTICS. 

Observations on Light and Vision, 333 — Catoptrics, 347 — Effects 
of Plain Mirrors, 348— Atmospheric Reflection, 351 — Convex Mirrors, 
354 — Concave Mirrors, 358 — Dioptrics, 362 — Optical Lenses, 368 — 
Organs of Vision, 373 — Theory of Vision, 375 — Chromatics, 384 — 
Chromatic Refraction, 387 — Rainbow, 395 — Varieties of optical Instru- 
ments, 407 — Spectacles, 407 — Microscopes, 411 — Telescopes, 412 — 
Double Refraction and Polarization of Light, 413— Works on Optics, 41 7 

ELECTRICITY. 

Miscellaneous Observations, 418 — Theory of Electricity, 421 — Con- 
ductors and Non-conductors, 425 — Induction, 427 — Electrical Instru- 
ments and Experiments, 429 — Electro-galvanism — Electro-magnetism, 
451 — Terrestrial Magnetism, 459 — Variation of the Compass, 461 — 
Works on Electricity, 462— Index, 463. 



PREFACE 



The extensive adoption in the United States of that, 
system of education which regards useful Imowledge 
as indispensable to a useful life, necessarily calls for 
the preparation of treatises adapted to the requisitions 
of those who are to impart as well as to the wants of 
those who are to receive such knowledge. Not only are 
elementary works demanded, but they must occasionally 
be remodelled with a view to the advancement of the 
sciences to which they relate. To adhere pertinaciously 
to the text books of the last century would be to do 
equal injustice to the state of education and to the pro- 
gress of human knowledge. To suppose that the 
labours of the learned have, within the last quarter of 
a century, resulted in no modifications of elementary 
laws, as enunciated at the beginning of that period, 
would be to contradict the plainest evidence of daily 
observation. The physical sciences have, within this 
period, enjoyed a most vigorous growth. Not content 
with the bare discovery of a law and the enunciation 
of it as among the maxims hereafter to be received as 
truth, the views of men of science have become habi- 
tually directed to the harmonizing of the known and 
received laws, into more general and comprehensive 
expressions of nature's vast designs. By this course of 
proceeding, the mind is not only enabled to embrace 
wider ranges of thought, and more rational speculative 
views in each department or branch of science, but in 
several instances to include under one department the 
facts and phenomena previously regarded as constitut- 
ing several distinct sciences. Thus while the inductive 
labours of Galvani and Volta laid the foundation, as 
they (and as all the world) supposed, for a new science, 
the recent researches of philosophers have wellnigh 



6 PREFACE. 

resolved not only that, but two or three other sciences 
into one general principle of action, variously mani- 
fested according to the circumstances of each particular 
case. While this process of enlarging and clearing the 
views of men in regard to general truths in science has 
been advancing, there has been a constant and zealous 
vigilance displayed in reference to the practical applica- 
tions of knowledge to the great physical and social 
purposes of man. These purposes can be fully sub- 
served, only by keeping the public mind apprized of 
all the important steps taken in the advancement of 
those sciences which are susceptible of a practical 
application. Natural Philosophy, Chemistry, and seve- 
ral branches of Natural History, are, of all departments 
of human knowledge, those which have most engaged 
the attention of modern philosophers ; and it is with a 
view to the present state and the useful employment of 
these sciences, that the publishers of the Scientific Class 
Book have sought to furnish the schools and academies, 
no less than the private students of the United States, 
with an appropriate and eligible manual. 

In selecting for the basis of such a manual the text 
of Mr. Moffatt, it was with the full understanding 
that in order to be adapted to the purposes of instruc- 
tion here it must be somewhat varied from its English 
dress. Some inaccuracies in the statement of facts and 
principles were easily perceived ; some grave errors 
in regard to persons, places, and things, especially in 
this country, were at once discovered, a number of im- 
portant discoveries and inventions due to the citizens 
of the United States were w r holly overlooked ; several 
long notes in Latin not likely to interest the young 
reader had been introduced ; the allusions to local 
objects and occurrences which pervaded the work 
seemed to require more oral explanation than the 
student in any other place than London was likely to 
receive ; the puerile cuts which headed the chapters 
in the English editions, and which have conveyed to 
many persons the idea that the compilation was intended for 
very young children, were conceived to be less useful 



PREFACE. 7 

than some additional figures illustrating the topics 
treated in the work. In the above-mentioned particu- 
lars, the work was thought to require emendation. 

But as the several treatises appeared in the main to 
have been compiled with a view to the best authorities, 
as well as in a style sufficiently simple and perspicuous 
to warrant an attempt to adapt it to the purposes here 
intended, the publishers were induced to believe that 
they could not offer to teachers and students a more 
acceptable addition to the means of instruction than the 
work now presented for their consideration. 

The general practice of introducing into class-books 
questions for examination is so well established as to 
need little comment. Yet not every kind of questions 
can render a text-book more valuable than it would be 
without them. It has been the aim of the editor so to 
execute this part of his duty, as to lead the student into 
habits of reflection on the true nature and bearings of 
the subject before him, not to confine his attention while 
answering the queries merely to certain words of the 
text ; — to excite the industry of the pupil, rather than 
increase the labour of the teacher ;— to enable the stu- 
dent to rise from his task with clearer conceptions of 
things, than he enjoyed before attempting to answer 
these questions, not to deceive either himself, his 
teacher, or others, by a show of knowledge which he 
does not possess. In some cases hints and suggestions 
are conveyed by the same means, and the application 
of certain terms not contained in the body of the work, 
will be easily understood from the manner in which 
they are introduced into the questions. The answers 
will occasionally be inferences and deductions, gene- 
rally easy to be made, from the facts and principles 
contained in the text. In these cases the mind will, it 
is conceived, find a more pleasing and profitable exer- 
cise than in the mere repetition of statements found on 
the page to which these questions refer. 

At the end of every important division of the subject 
is presented a list of such works as may be found 
useful to those who desire to prosecute particulai 



PREFACE. 

inquirj 



quiries relating to the part immediately preceding. 
A few works in foreign languages are included in the 
number, and as the French language in particular is 
now so extensively read at least among teachers, it is 
believed that references to them will by no means 
prove useless. The index will, it is hoped, prove 
entirely adequate to the purpose which it is designed 
to subserve. 

In conclusion it may be observed that, whatever 
merit may be claimed for other treatises on the same 
departments of science, it is confidently anticipated that 
this will be found to embrace as full and satisfactory a 
view of the subject which it proposes to treat, as any 
similar compilation, which has hitherto been dedicated 
to the service of American youth. In this hope the 
publishers respectfully submit it to the consideration 
of the reader. 

Cd- The publisher has deemed it advisable to adopt a new title 
for this book, setting forth more clearly the particular branches 
of science of which it treats, and this change is rendered expedient 
by the further consideration that there is another work of a totally 
different character published in this country, called the Scientific 
Class Book. 



INTRODUCTION. 

1. Among the several distinctions which have been made in 
human knowledge, those of most importance to be noticed in the 
commencement of the present work, regard the discrimination 
between the mathematical and the physical sciences. The latter 
are so far dependent on the former, that some knowledge of ma- 
thematics is absolutely necessary, previously to entering to any 
extent on the study of physical or natural philosophy. A gene- 
ral acquaintance with at least the elementary branches of mathe- 
matics, as arithmetic, geometry, and trigonometry, may be ex- 
pected to have been acquired by all tolerably well educated per- 
sons, as usually forming a part of a common school education. 
Physical science, or natural philosophy, constitutes the exclusive 
object of the present volume, in order to the perusal of which, 
with profit and advantage, it will be requisite that the reader 
should not be ignorant of the names and general properties of 
geometrical lines and figures. The following diagram and ex- 
planatory observations are therefore introduced, as they may be 
useful to those who are but slightly acquainted with mathema- 
tics, and may sometimes save the better informed student the 
trouble of referring to other books for information, respecting the 
signification of particular terms. 




A a Circle. 
A a its Diameter. 
B the Radius. 
C a Chord. 
D an Arc. 
E a Tangent. 
F a Secant. 
G a Co-tangent. 
H the Sine of Arc a b. 
I the Co-sine. 
K the Versed Sine. 
L the Sine of complemental Arc b c. 



2. Every circle is supposed to be divided into 360 degrees, 
and the line which bounds the circle, and on which therefore 
these degrees may be marked, is called its circumference. Any 
lines equidistant from each other throughout their whole extent 

Describe the several parts of the diagram represented in the margin. 
Into how many degrees is a circle supposed to be divided ? 
What are parallel lines ? 

9 i 



10 INTRODUCTION. 

•are termed parallel lines. Two lines not parallel but in the same 
plane must, if sufficiently produced, meet in a point, which is 
called an angle. Angles are principally distinguished by the re- 
lative inclinations of the lines by which they are formed. When 
one line meets or crosses another perpendicularly, the angles they 
form are called right angles ; and any angle smaller than a rig-lit 
angle, is styled an acute angle, and any greater an obtuse angle. 
But angles are more precisely measured by reference to the num- 
ber of degrees contained in an arc of a circle joining the two 
lines by which an angle is formed. Thus a right angle mus^ be 
included within an arc of a circle equal to a quadrant, or the 
fourth part of 360 degrees, namely, 90 degrees ; and an acute 
angle included within an arc only half the extent of a quadrant 
will, of course, be an angle of 45 degrees. 

3. A space or flat surface, inclosed by three lines, is the most 
simple of all definite figures, and is called a triangle. Among 
the varieties of these figures are the rectangular triangle, so 
named because it has one right angle ; the equilateral triangle, 
which has three sides of equal extent; the isosceles triangle, 
which has only two equal sides ; and the scalene triangle, all the 
sides of which are of different lengths. Any space inclosed by 
four lines is called a quadrilateral, or four-sided figure. Among 
such are included the square, having four equal sides and right 
angles ; the rectangle, or oblong square, having only the opposite 
sides equal; the lozenge, which has equal sides and unequal an- 
gles; and the trapezium, which has only two of its sides parallel. 
When the sides of a quadrilateral figure are parallel, it is termed 
a parallelogram. Aline joining two opposite or alternate angles, 
is called a diagonal. Any figure having several angles, and con- 
sequently several sides, is named a polygon. 

4. Solid figures include the tetraedron, or four-sided solid, 
which is the most simple figure of the kind, as no solid can have 
less than four sides; and when the number of sides is greater, the 
figure is called eitherahexaedron,anoctaedron,anicosaedron,ora 
polyedron, according to the number of its sides. 

5. Among polyedrons may be distinguished the prism, formed 

What constitutes an angle ? 

By what names are different angles distinguished ? 
How are they accurately measured ? 

How many degrees of a circle are contained in a right angle r* 
What is the most simple definite figure ? 

What is a rectangular triangle? an equilateral triangle? an isosceles 
triangle ? a scalene triangle ? 

What is a four-sided figure called ? 

Describe some of the figures that come under this denomination. 

What is a diagonal ? 

What is a polygon ? 

What is the most simple of solid figures ? 

How many sides has a hexagon ? 

How many an octagon ? an icosaedron and a polyedron ? 

Of what form is a prism ? 



INTRODUCTION. 1 1 

of parallelograms only, dr of parallelograms and two polygons of 
any number of sides. Among the prisms may be specified the 
parallelepiped, formed of six parallelograms only; and among the 
parallelopipeds may be noticed the cube, having six square sides. 
The pyramid is apolyedron, formed by a polygon of any kind as 
its base, and as many triangular planes as the polygon has sides .: 
the point where all the triangular planes unite is called the sum- 
mit of the pyramid. The most simple solid of this kind is the 
tetraedron, or four-sided pyramid, including the base. 

G. The terms sphere, cylinder, and cone, designate solid figures, 
having either entirely or partially curved surfaces ; and the ex- 
pressions spheriod, cylindroid, and conoid, are used to denote 
solid figures, more or less resembling a sphere, a cylinder, or a 
cone, respectively. 

Natural Philosophy is the science which explains the causes of 
the various properties of .bodies in general, as shown by the 
changes which they undergo in any particular circumstances, or 
the changes which they may occasion in other bodies, under cer- 
tain circumstances. The province of natural philosophy does not 
extend to the explanation of the doctrine of final causes, or the 
immediate and positive reasons why particular effects take place, 
or why certain bodies possess the peculiar properties with which 
they are endowed; but it enables us to appreciate the conse- 
quences of any body being placed in a given situation, or to fore- 
tel what will be result of any body acting on another in a certain 
manner. 

7. Thus, we know nothing of the absolute cause of gravity or 
weight, which is that property of bodies in consequence of which 
they fall towards the surface of the earth, if raised in the air by 
any force and then dropped; but natural philosophy, while it 
leaves us in ignorance of the final cause of gravity, enables us to 
determine a vast variety of curious circumstances with respect to 
falling bodies. Thus, it is found that a heavy body, as for in- 
stance a marble or a musket-ball, dropped from a high tower, 
would fall faster as it approached near to the ground than it 
would in passing through the former part of its descent; and the 
rate at which a body falls through a given space has been ascer- 

How is the parallelopiped formed ? 

How many sides has a cube ? 

How is a pyramid formed ? 

Where is the summit of a pyramid ? 

What is the most simple solid of this kind ? 

What kind of figures are designated by the terms sphere, cylinder, 
and cone ? 

How are those figures denominated that more or less resemble these 
figures ? 

What is Natural Philosophy ? 

What are some of the doctrines beyond the explanation of Natural 
Philosophy. 

What is there in the subject of gravity which is inexplicable by na- 
tural philosophy, and what does this science enable b«. u o -teffeiine res- 
pecting it ? 



12 INTRODUCTION. 

tained by experiment, and can be calculated with the utmost ex- 
actness. 80 as to the final cause of electric and magnetic attrac- 
tion various opinions have been advanced, and it is still involved 
in obscurity ; but we know by experience that a magnet attracts 
iron with considerable force, and that a thin bar of magnetic iron, 
accurately poised on its centre, will, when left free, point towards 
the north with one end, and towards the scuth with the other ; 
and on the latter property depends the action of the mariner's 
compass, by means of which the sailor, crossing the pathless sea, 
is able to ascertain in what direction his vessel is steering; and 
to this little instrument, which was unknown to the ancients, we 
are in a great degree indebted for the important discoveries of 
modern navigators. 

8. Whether light and heat are owing to matter or motion has 
been left among the questions which philosophy has hitherto 
been unable satisfactorily to decide; but the effect of light on bo- 
dies, whether opaque, transparent, or semi-transparent, the velo- 
city with which it passes through space, and the manner in which 
it is modified by optical glasses of various forms, are among the 
numerous interesting and surprising properties of light, which 
natural philosophy has laid open to our investigation, and which 
we are enabled to verify and illustrate by means of mathematical 
calculation; and the phenomena of heat and cold, with which we 
are so intimately familiar, from the sensations they occasion, are 
equally hidden as to their final cause, and equally wonderful and 
curious as to their effects, the latter of which alone afford an am- 
ple field for the experiments and deductions of the philosophical 
inquirer. 

9. Astronomy presents a boundless field for research, and not- 
withstanding it has been explored with signal success in modern 
times, yet the most important discoveries that have been made 
onl}' serve most distinctly to evince that the wisest and most suc- 
cessful investigators of the phenomena of the science have merely 
entered on the confines of knowledge, and enabled us to form 
some imperfect estimate of those boundless regions which display 
an inexhaustible field for future speculation and inquiry. It has 
indeed been ascertained that the sun and the planetary and other 
bodies wmich constitute the solar system, are influenced by the 
same moving power as that which causes the fall of an acorn to 
the ground, when detached from the oak on which it was pro- 

What has experience taught respecting magnetic and electric attrac- 
tion ? 

What question respecting the nature of light and heat has been hi- 
therto undecided by philosophy ? 

What are some of the properties of light which natural philosophy 
has laid open to our investigation, and how are these to be verified ? 

In regard to heat, what points are known and what unknown ? 

What conclusions have been drawn from the most successful investi- 
gations in astronomical science ? 

What has been ascertained to be the moving power that influences the 
oodies of the solar svstem ? 



INTRODUCTION'. 13 

duced; and that the attractive force which retains the moon in he* 
orbit, and causes her reaction on the fluid parts of the terrestrial 
globe we inhabit, producing the tides, may be estimated with ac- 
curacy, and subjected to mathematical calculation. But there 
are numberless topics of inquiry — with regard to the constitution 
of the sun, the nature of comets, and the causes of their peculiar 
motions, the kind of medium which occupies the space beyond 
the atmospheres of the earth and planets, and the relations that 
may exist between our solar system and the numberless other 
systems, the existence of which may be inferred from the appear- 
ance of the starry heavens — which may for an indefinite period 
serve to exercise the talents of men of genius and learning, but 
concerning which we can hardly hope to attain any knowledge 
approaching to certainty, till discoveries and inventions in other 
sciences provide us with means for investigating the works 
of nature, as much superior to those which we at present possess, 
as our instruments of research surpass those employed by the 
ancients. 

10. "The proper business of philosophical inquiry," says 
Leslie, "is to study carefully the appearances that successively 
emerge, and trace their mutual relations. All our knowledge of 
external objects being derived through the medium of the senses, 
there are only two ways of investigating physical facts — by ob- 
servation or experiment. Observation is confined to the close inves- 
tigation and attentive examination of the phenomena which arise 
in the course of nature ; but experiment consists in a sort of ar 
tificial selection and combination of circumstances, for the purpose 
of searching minutely after the different results. 

11. "The range of observation is limited by the position of the 
spectator, who can seldom expect to follow nature through her wind- 
ing and intricate paths. Those observations are of the most value 
which include the relations of time and space, and derive greater 
nicety from their comprising a multiplied recurrence of the same 
events. Hence Astronomy has attained a much higher degree of 
perfection than the other physical sciences. 

12. " Experiment is a more efficient mean than observation for 
exploring the secrets of nature. It requires no constant fatigue of 
watching, but comes in a great measure under the control of the 
inquirer, who may often at will either hasten or delay the expected 
event. Though the peculiar boast of modern times, yet the method 

What is the effect of this force upon the moon, and indirectly upon 
the earth ? How are these effects to be estimated ? 

What subjects of inquiry in astronomical science, are supposed to lie 
beyond our present means of investigation ? 

What does Leslie affirm to be the proper business of philosophical in- 
quiry ? 

What are the only two methods of investigating physical facts, and 
what is the province of each ? 

What circumstance limits the range of observation ? 

What observations are of most value ? 

Which is the more efficient means of exploring the secrete of niiture ? 

B 



14 INTRODUCTION. 

of proceeding by experiment was not wholly unknown to the an- 
cients, who seem to have concealed their notions of it under the veil 
of allegory. Proteus signified the mutable and changing forms of 
material objects ; and the inquisitive philosopher was counselled 
by the poets to watch that slippery dasmon when slumbering on 
the shore, to bind him, and compel the reluctant captive to reveal 
his secrets.* This gives a lively picture of the cautious and intre- 
pid advances of the skilful experimenter. He tries to confine 
the working of nature — he endeavours to distinguish the seve- 
ral principles of action — he seeks to concentrate the predominant 
agent — and labours to exclude as much as possible every disturb- 
ing influence. By all these united precautions, a conclusion is 
obtained nearly unmixed, and not confused, as in the ordinary 
train of circumstances, by a variety of intermingled effects. The 
operation of each distinct cause is hence severally developed."! 

13. The object of Natural Philosophy may be stated to be the 
study of the general properties of unorganized bodies, or inert 
substances in the state of solids, liquids, airs, or gases, and those 
which have been termed incoercible or ethereal fluids. It is also 
within the province of the physical sciences to examine the me- 
chanical action which bodies, in their different states, may exer- 
cise on each other, and the different circumstances connected with 
their movements. 

14. The various effects of the motions and operations of bo- 
dies depending on their general properties have hence been made 
the foundation of several distinct sciences or branches of know- 
ledge, which have been usually classed with reference to the se- 
veral forms of matter called solids, liquids, and airs, or to certain 
kinds of phenomena, supposed to depend respectively on the pre- 
sence and action of some imponderable modification of matter or 
ethereal fluid, to which have been referred thermometrical, optical, 
electrical, and magnetic phenomena. Hence a treatise on Natural 
Philosophy may be conveniently arranged under the different de- 
partments of (1.) Mechanics, or the doctrine of equilibrium and 
motion as respects solids, including Statics and Phoronomics or. 
Dynamics ; (2.) Hydrostatics, including Hydrodynamics or Hy- 
draulics, relating to the equilibrium and motion of liquids ; (3.) 
Pneumatics, including Aerostatics, and Aerodynamics, or the 
effect of forces on air and other gaseous fluids ; (4.) Acoustics, or 
the theory of sound, comprehending observations on musical and 
vocal sounds; (5.) Pyronomics, or the investigation of the causes 
and effects of heat, or more generally of change of temperature ; 

What is the object of Natural Philosophy ? 
How have its divisions been formed ? 

What are the different departments under which a treatise on Natural 
Philosophy may be properly arranged ? 

Of vhat does each of these departments treat ? 

* "V Virgil. Georgic. lib. iv. 

t Introduction to Elements of Natural Philosophy. 



INTRODUCTION. 15 

(6.) Photonomics or Optics, including- the theory of light and 
vision ; (7.) Electro-magnetism, which treats of the causes of 
electric and magnetic attraction and repulsion. 

15. The idea of absolute or indefinite space is obtained by ab- 
straction, or conceiving in imagination the absence of all bodies, 
or of all the properties of matter. Every part of this space, or 
rather of this imaginary void or vacuum, which can be conceived 
to be included in any way between limits, is called relative space. 
The term body is used to designate limited extension, to which are 
attached any of the properties of matter. That which distinguishes 
in general a simply extended body from a void space or vacuum, is 
the property of impenetrability, that is, the quality in consequence 
of which a body occupies a certain space, and excludes from it all 
other bodies. 

16. We acquire a knowledge of the properties of matter through 
our senses, either by immediate observation, or by experimental 
inquiry with the aid of instruments. The senses of sight and feel- 
ing afford us abundance of information concerning the properties 
of bodies around us, but our knowledge may be vastly extended 
when we assist the former by means of optical glasses, which open 
new worlds to our view, or when by means of delicate instruments 
we measure degrees of temperature, electricity, or magnetic power. 

17. Solid bodies are those which, like stone or wood, present a 
sensible resistance when touched, pressed, or handled. They 
may be cut into various forms, and preserve without difficulty the 
figures which are given to them, or which they possess naturally. 
Sand, powders, and similar substances consist of small particles 
not united together; yet though, collectively, masses of sand present 
but little resistance to pressure, the individual minute particles 
have all the characteristics of solid matter, and though readily 
dispersed by force, they may be assembled in heaps more or less 
considerable. 

18. Liquid substances are those which, like water, manifest 
immediately to the touch but a very feeble resistance, but quite 
sufficient to indicate their presence, even when in a state of repose. 
They cannot be grasped between the fingers like solid bodies, nor 
can they be collected in heaps, or made to take any particular 
figure, except that of the vessel in which they may be included. 

19. Aeriform fluids are in general invisible bodies, which like 
the air surrounding us cannot be felt, and afford no evidence of their 
presence to the sense of touch when in repose. But their existence 
is ascertained with abundant certainty when they are in motion ; 
thus no one can doubt the materiality of atmospheric air aftc 

How do you obtain an idea of absolute or infinite space ? 
What is relative space ? 
What is meant by the term body? 
What is the property of impenetrability ? 

By what means do we acquire a knowledge of the properties of mat- 
ter ? 
What are solid bodies ? liquid substances ? aeriform fluids ? 



18 INTRODUCTION. 

experiencing the violent exertion necessary in walking against a 
high wind. Aeriform bodies may be confined in vessels, whence 
they exclude liquids or other bodies, demonstrating their impe- 
netrability, though they readily become compressible to a great 
extent, but there are limits beyond which it is impossible to 
reduce them. 

20. Incoercible or imponderable fluids do not manifest their 
existence by the exhibition of impenetrability or weight, which 
have usually been regarded as essential properties of matter; and 
they must, therefore, be considered as hypothetically admitted, in 
order to account for certain phenomena, which appear to depend 
on the presence and action of one or more ethereal media. — 
That light is such an imponderable fluid, emanating from the sun, 
was one of the generally received doctrines of the Newtonian 
Philosophy; the caloric or matter of heat of the French chemists 
was supposed to be a fluid of a similar nature ; and men of science 
who have written concerning magnetism and electricity have 
vaguely employed the terms magnetic fluid and electric fluid to 
designate the unknown causes of the phenomena they describe. 

21. At present it is perhaps the more prevalent opinion of phi- 
losophic inquirers that there exists at least one kind of ethereal, 
imponderable medium, the different modifications and modes of 
action of which give rise to the various phenomena of light, heat, 
and electro-magnetic attraction and repulsion. Thus it may be 
supposed that as sound is conveyed to our ears by the vibrations of 
the air, so light affects our eyes through the immensely more 
rapid vibrations of the electro-luminous ether. The existence of 
such a medium, manifesting neither weight nor impenetrability 
capable of being appreciated by the most delicate instruments, may 
be fairly inferred from the movements which take place in bodies 
under certain circumstances when all the ponderable and coercible 
kinds of matter have been carefully excluded, and these move- 
ments therefore must be ascribed to the presence of an ethereal 
influence, which can penetrate glass and other dense substances 
which are impervious to the rarest gases or most attenuated and 
subtile vapours with the existence of which we are acquainted. 

22. But such speculations, if not rather curious than useful, 
would, if extended, be incompatible with the plan and objects of 
the present Avork. Therefore, though it would have been improper 
to have omitted all mention of them, they must be dismissed for 
the present, with the preceding short notice ; especially as oppor- 
tunities for resuming them will occur in some of the ensuing 
treatises. 

How is their existence ascertained, and how is their impenetrability 
demonstrated ? 

How do the incoercible or imponderable fluids differ from these ? 

What have hitherto been considered imponderable fluids? 

What is the present more prevalent opinion respecting the imponder- 
able medium ? 



MECHANICS 

i. There is perhaps no department of Natural Philosophy of 
such extensive importance as Mechanics, since its principles are 
founded on those properties of matter which are among the most 
obvious and essential, — namely, Mobility and Weight ; and the 
effects produced by the operation of these properties are so dis- 
tinct and certain, that they can be subjected to mathematical cal- 
culation. Hence Dr. Wallis has described Mechanics, with 
some degree of propriety, as the " Geometry of Motion." 

2. The designation of this branch of knowledge, like most 
other scientific terms, is derived from a Greek word,* signifying 
a Machine ; and Mechanics may be considered as the Philosophy 
of Machinery, or the Theory of Moving Powers. Many writers 
have treated of this science under two heads, regarding those 
principles which relate to the gravity or weight and to the equi- 
librium of bodies, or the powers which preserve bodies in the 
state of rest, as the subject of the doctrine of Statics ; j" and the 
principles relating to the causes of movement, or the forces pro- 
ducing motion, acting by means of solids, as forming the subject 
of the doctrine of Dynamics. :£ But, as the respective states of 
bodies at rest, and bodies in motion, may be most correctly con- 
sidered as the consequences of different modes of action of the 
same causes, they may be instructively illustrated by showing 
their relations to each other, for which reason it will be proper to 
treat of them in conjunction, rather than separately. 

3. From this statement of the nature and objects of Mecha- 
nics, it will at once appear that we have by no means overrated 
the importance of an acquaintance with this science to the Stu- 
dent of Natural Philosophy. For all motions are more or less 
subject to the laws of Mechanics, and without a knowledge of 
those laws, it is impossible to appreciate the effects, or calculate 
the consequences, of those motions of the celestial bodies which 
occasion the phenomena of Astronomy ; or of those properties of 
fluids, whether liquid or gaseous, on which depend the principles 
of Pneumatics, Hydrostatics, and Hydraulics ; or indeed of any 
circumstances affecting the ponderable forms of matter. And 
those sciences which relate to Heat, Light, Electro-magnetism, 

Upon what properties of matter are the principles of mechanics 
founded ? 

What definition is given of mechanics ? 

Under what heads has this science generally been treated ? 

How extensive is the application of mechanical principles to other de- 
partments of science ? 

f From the Greek verb Zt«o, to stand, or be fixed ; or from Sraowf, 
the act of standing. 

| From the Greek word Aui/a«< s , power or force. 

R 2 17 



18 MECHANICS 

Vital Power, cither in Animals or Vegetables, or any other phe- 
nomena which appear to be independent of the force - of gravita- 
tion, yet derive most important aid from Mechanics ; for it is 
chiefly by means of mechanical instruments that the influence of 
heat, light, electricity, magnetism, or the effects of vitality, as in 
the motion of the blood in animals, or of the sap or other fluids 
in vegetables, can be estimated. Mechanics may, therefore, be 
considered as the basis or groundwork of the other Physical 
Sciences, or branches of Natural Philosophy. 

4. Previously to entering on the consideration of the Theory 
of Mechanical Powers, it will be necessary to show the nature 
and effects of Mobility, or the capacity for motion, and of Weight, 
or the gravitation of bodies, — as these are the general properties 
of matter on which, as already stated, the phenomena of Mecha- 
nics depend. 

Mobility. 

5. Every individual body, or portion of matter, must take up 
a certain space. This may be considered as the absolute place 
of the body, in reference to its situation simply and singly ; or 
as its relative place, or situation with respect to other bodies. 
The relative situation of a body may be changed either by its 
own motion, or by the motion of the bodies around it. A body 
may exhibit the appearance of actual motion, or absolute change 
of place, while it remains at rest, its change of place being only 
relative. Thus, the Moon, when a train of thin fleecy clouds is 
passing over its face, if we attentively fix our eyes on it, seems 
to move, and the clouds to stand still, though this is only an ap- 
parent motion of the Moon, in a direction contrary to that in 
which the clouds are really moving. And if we hold a common 
eyeglass, or any transparent substance, a few inches before the 
eyes, and move it backwards and forwards, looking through it at 
any object, as an inkstand or knife, which remains unmoved, it 
will, as in the former case, exhibit an apparent motion, arising 
from the actual movement of the glass. 

6. Mobility is the capacity of a body for change of place by 
its own motion, it therefore infers the capability of real or actual 
motion, and not of relative motion only. Yet this change of 
place may sometimes be most readily estimated by the conse- 
quent relative motion which accompanies it. Thus, a person 
sailing in a boat on a smooth stream, or going swiftly in a coach 
along an even road, would hardly perceive the motion of the ve- 
hicle except by the change of scene, and trees or buildings on 
the banks of the stream, or by the road-side, would seem to move 
in an opposite direction from that of the real motion of the boat 
or carriage. Every tolerably well-informed person now admits 

i 
What is meant by the absolute place of a body ? 
What by the relative ? 
What is mobility? 



MOTION. 



19 



that the earth moves, and the sun stands still ; but the motion of 
the former is not perceptible, and the apparent daily motion of 
the latter, being so obvious to our senses, was, till within the 
last three centuries, considered as a real motion, the existence of 
which could not even be questioned with impunity. 

7. Without some active cause motion can neither commence 
nor cease ; since a body in the state of rest would always remain 
unmoved, if never subjected to the influence of a moving force, 
and on the contrary, a body when set in motion would go on t 
move for ever, if it met with no opposition to its progress. I 
may seem inconsistent with this doctrine, that any body set ii 
motion, within the range of our observation, will continue to 
move without a fresh impulse for a time, but at length will slacken 
its speed, and finally resume the state of rest. Thus, a cannon- 
ball will pass a certain distance when discharged from the mouth 
of a cannon, but if it does not strike a solid body, still it will 
ultimately fall to the ground ; and a marble or a cricket-ball 
thrown forwards with the hand, if it meet no obstacle, will reach 
only a certain distance, proportioned to the force used in throw- 
ing it. 

8. In both these and all similar cases, the termination of the 
motion of the moving body is owing chiefly to two causes. The 
first of these is gravitation towards the earth's centre, common 
to all bodies, and which constantly tends to keep them at rest, 
pressing on the surface of the earth with a degree of force pro- 
portioned to their weight and bulk ; or, if, as in the case of the 
cannon-ball, they pass through the air, the force of gravitation 
then tends to draw them continually nearer to the earth, till at 
length they fall and rest upon it. But the second and more ob- 
vious cause of the decay of motion is the resistance of the me- 
dium through which the moving body takes its course ; and thus, 
a body moving through the air, like the cannon-ball, gradually 
becomes less and less able to pass forward till its moving force 
is destroyed. It will be readily perceived, that the resistance of 
the medium to the body which passes through it, must depend 
much on its density or consistence ; thus, a ball driven by a cer- 
tain force would pass further through the air than through water, 
and further through the latter than through a denser fluid, as 
brine or syrup, or through solids, as sand or clay. 

9. Another circumstance which will affect the motion of a 
body, with relation to the medium through which it travels, must 
be taken into the account, and this is the form of the moving 
body. A small body will meet with less resistance than a large 
one of the same weight ; and a body which presents an extensive 

State some familiar examples, and show how real and apparent motioa 
may best be distinguished. 

How is a body at rest to be put in motion, and when in motion, how 
brought to rest ? 

What other circumstances go to retard or accelerate the motion of 
bodies ? 



20 MECHANICS. 

surface to the medium through which it moves, will be retarded 
in its passage much more than one with a small surface. A 
sheet of paper stretched out to its full extent, and suffered to fall 
a few feet, and then folded up into a small compass, and again 
suffered to fall from the same height, will afford an exemplifica- 
tion of the resistance of the atmosphere to falling bodies ; and 
an illustration of a different kind, but to the same purpose, may 
be drawn from the advantage which sharp-edged and pointed in- 
struments have over blunt ones in penetrating hard or tough sub- 
stances. A body moving in contact with a solid substance, as 
when it is rolled or dragged along the ground, is also affected by 
friction. This obstacle to motion is proportioned to the rough- 
ness or smoothness of the surface over which the body passes : 
thus, a marble thrown with any given force will run much fur- 
ther along an even pavement, than along an equally level gravel 
walk ; and still further along smooth ice. Here again the form 
of the moving body has much influence on the velocity and ex- 
tent of motion ; for the fewer the points of contact between the 
surface and that which passes over it, the more freely will motion 
take place.* 

10. All bodies subject to our control are exposed to the opera- 
tion of gravity, in various degrees, and from this cause, inde- 
pendent of the resistance of the medium which they traverse, or 
of the effect of friction, their motions cannot be indefinitely con- 
tinued, but must decline and terminate in a given time, according 
to the circumstances in which they are placed. But though per- 
petual motion cannot be exhibited by any methods which human 
skill or industry can contrive, yet we have continually before us 
the display of bodies which have been moving with undiminished 
velocity for ages past, and which no power but that which go- 
verns all nature can prevent from moving in the same manner for 
innumerable ages to come. The bodies to which we refer, as 
will probably be anticipated, are those whose motions are the ob- 
jects of the science of Astronomy ; and though that subject will 
not come under our immediate discussion, yet the general nature 
of the forces which occasion the revolution of the celestial bodies 
will be explained, and the causes of their uniform and uninter- 
rupted motion will be illustrated. 

11. That state of bodies just described, in which motion or 
the cessation of motion can take place only in consequence of an 
extraneous cause, has been termed Inertia, which signifies inac- 

What are some of the examples which illustrate this point ? 

What other cause is there, independent of these, which operates upon 
all bodies, limiting their motion and precluding the possibility of perpe- 
tual motion by human skill ? 

What is inertia? 



* This statement is to be understood as limited by the greater or les9 
difficulty with which the surface can be abraded. 



MOTION. 21 

tivity, equally opposed to motion when at rest, and to rest when 
in motion ; so that if a given force is required to make a body 
move with a certain velocity, the same force will be required to 
destroy its motion. When a garden roller is being drawn along 
a level surface, the exertion necessary to stop it suddenly, at any 
given point, would be precisely the same as would be required 
to move it backward, if it were at rest, and of course the same 
that was applied to set it in motion at first. 

12. Any force applied to produce motion may be called Power 
or impulse, which may be either continued, as in the case of 
pressure, or intermitting, as in the case of impact or percussion. 
Whatever opposes motion so as to retard the moving body, destroy 
its motion, or drive it in a contrary direction, may be termed Re- 
sistance, and its effect, reaction or counteraction. It is one of 
the laws of motion that action and reaction are always equal and 
contrary. Thus, in pressing down the empty scale of a balance, 
while the other scale held a five pound weight, it is obvious that 
the force exerted must be equal to five pounds ; but if one scale 
had been loaded with fifteen pounds, and the other with only ten, 
the equilibrium might still be preserved by pressing on the latter 
with a force equal to five pounds only. And if a man, sitting in 
a boat on a canal, draws towards him, by means of a rope, 
another boat of equal weight, they will meet at a point half-way 
from the places whence they began to move. Suppose, however, 
the second boat to be so laden as to be twice the weight of the 
first, it must move the slower of the two, and consequently the 
point of meeting would be nearer the second boat than the first. 
If a body in motion strikes another body of equal mass at rest, 
the two bodies will move together, but with only half the original 
velocity of the first, the other half having been expended in over- 
coming the inertia of the second body. Corresponding effects 
will take place, whatever difference there may be between the 
masses of the two bodies ; for if the second body should be dou- 
ble the mass of the first body, the common velocity after the im- 
pact of the two bodies would be one-third that of the first ; and 
if the. mass of the first body be to that of the second, as 5 to 7, 
the common mass after impact will be 12 ; and as the second will 
deduct from the motion of the first in proportion to its mass, the 
motion lost by the first body will be seven-twelfths, and the mo- 
tion retained would be five-twelfths. 

13. If two bodies are both in motion in the same direction, and 
one overtake and impinge on the other, suppose the masses of the 
two bodies to be the same, and the velocity of the first to be 7, 
and that of the second to be 5, their common velocity after im- 
pact will be 6, or half the sum of the two velocities. But if the 
masses are unequal, the mass of each must be multiplied seoa- 

What is poioer? 

What resistance ? 

What is one of the laws of motion ? 

Give some of the illustrations. 



22 MECHANICS. 

rately by its velocity, and the products added together, and their 
sum divided by the sum of the two masses will give the common 
velocity. When two bodies are moving in opposite directions, 
with the same velocity, and having equal masses, action and re- 
action being equal, both motions will be destroyed. Suppose, 
however, the masses to be alike, and the velocity of the first 
body to be 10, and that of the other to be 6, the first body will 
lose 6 parts of its velocity, which will be requisite to neutralize 
or destroy the opposite velocity of the second body, and the re- 
maining 4 parts of the velocity of the first body being, divided 
between the two, they will move together in the direction taken 
by the first body with a common velocity equal to 2. 

14. When the masses, as well as the velocities, are unequal, 
the common velocity of two bodies after impact may be found 
by multiplying the numbers denoting the masses by those ex- 
pressing the velocities respectively, subtracting the less pro- 
duct from the greater, and dividing the remainder by the sum of 
the numbers denoting the masses : the quotient will then show 
the velocity with which the bodies will move together, in the di- 
rection of the body having the greatest quantity of motion. 

15. An experimental illustration of the equality of action and 
reaction in the collision of bodies may be thus exhibited : 

Suppose a and b to be two inelastic balls,* 
suspended together at c, by threads of equal 
lengths, so that they may be in contact when at 
rest ; and let debea graduated arc, over which 
the balls may oscillate freely ; then, if the ball 
b be moved a certain number of degrees towards 
e, and let fall so that it may impinge on the ball 
a, both together will move towards d, through a 
number of degrees proportioned to their com- 
mon velocity. 

Since it appears from the foregoing observations to be an esta- 
blished principle of Mechanics, that the force or impetus of a body 
in motion is to be estimated by its mass and velocity, it must be 
concluded that a body, the mass of which is very inconsiderable, 
may be made to act with the same force as another body the mass 



How do you find the common velocity of two equal bodies which im- 
pinge against each other ? state separately the cases where one of them 
is at rest before impact, when they move in the same and when in oppo- 
site directions. 

How do you find the common velocity after impact when the masses 
as well as velocity differ ? 

Describe the experiments which demonstrate the equality of action 
and reaction. 

* No substance in nature is wholly destitute of elasticity, but soft clay, 
which is among the least elastic of solid bodies, may be used to make 
the balls for the above experiment. 




ELASTICITY. 23 

of which is much greater, provided the smaller body has a velocity 
communicated to it greater than the velocity of the larger body 
in the same proportion that the mass of the latter surpasses that 
of the former. Thus, a pincushion weighing half an ounce might 
produce as great an effect as a cannon-ball weighing thirty-six 
pounds, provided the pincushion had 1152 times the velocity of the 
cannon-ball; for 1152 half ounces being equal to 36 pounds, it 
must be obvious that the velocity of the pincushion would be just 
so much greater than the velocity of the cannon-ball, as the mass 
of the latter would be greater than that of the former. 

16. Hence as the momentum or effect of moving force is to be 
estimated by the velocity of the motion and the weight or mass 
of the moving body taken together, it may be perceived how it 
happens that a small mass may produce an extraordinary effect 
when moving with great velocity. Thus, a tallow candle fired 
from a gun will pierce a deal board. On the other hand a great 
effect may be produced by a small velocity if the moving mass is 
extremely great. As for instance, a heavily laden ship of great 
burden, afloat near a pier wall, may approach it with a velocity so 
small as to be scarcely observable, yet its force will be sufficient 
to crush a small boatr 

17. When two bodies meet in consequence of moving from 
opposite directions, each body will sustain a shock as great as if 
one body at rest had been struck by the other with a force equal 
to the sum of both their forces. Suppose two persons of equal 
weight walking in opposite directions, one at the rate of two miles 
an hour, and the other at the rate of four miles, if they should sud? 
denly come in contact, each would receive a shock as great as if he 
had been standing still, and another had run against him moving 
at the rate of six miles an hour. In the ancient tournaments when 
mailed knights met in full career, prodigious must have been the 
shock when the collision was direct, and both would often be 
overthrown with a force proportioned to their joint weights and 
velocities. So when two vessels under sail run foul of each other, 
suppose one of them eight hundred tons burden, and the othei 
twelve hundred tons, their velocities or rates of sailing being 
equal, each would sustain a shock equal to that which a vessel 
would receive if at anchor, and struck by another vessel of two 
thousand tons burden, sailing at the same rate with the vessels in 
question. Yet though the shock would be the same, the conse- 
quences would be most disastrous to the smaller vessel, the other 
being protected in a greater degree from injury by its superior 
strength and bulk. 

18. Elasticity being a common property of matter, and many 
substances employed for a variety of purposes, as several kinds of 
wood and metal, possessing that property in a high degree, its 

What remarkable examples can be cited of the effect of momentum 
on bodies at rest ? 

What practical illustrations can be given of the effect of bodies en- 
countering each other when moving in opposite directions ? 



24 



MECHANICS. 



influence in modifying the operation of moving forces must not be 
neglected. 

The different effects exhibited by bodies almost inelastic and those 
which are highly elastic may be illustrated by the simple experi- 
ment of dropping a ball of soft clay or wax from any given height 
on a solid pavement, and then letting fall from the same height a 
ball of box-wood or ivory of equal weight with the clay. The 
first ball will give way to the pressure of the pavement, and become 
dented or flattened on the side on which it rests, while the latter 
ball will rebound from the pavement with a force proportioned to 
the height from which it fell. This resiliency or rebound, in an 
ivory ball, is partly occasioned by its giving way to the pressure 
of the pavement, but unlike the clay it recovers its shape almost 
instantaneously, its surface thus acting as a spring against the pave- 
ment. That a hard substance like ivory is compressed by striking 
against a similar substance, may be shown by making a small dot 
with ink on the surface of one ball, and then bringing it gently in 
contact with another ball at that point, when a small mark will 
also appear on the latter ball ; but if the balls, one being marked as 
before, be brought into contact with considerable force, as by 
pressure or collision, a much larger mark will be found on the latter 
ball than before ; proving that, though both have recovered their 
shape, they must have undergone compression. 

19. Let two ivory balls of equal weight, a b, 
be suspended by threads, as in the annexed 
figure, if the former be then drawn aside to 
and suffered to fall against the latter, it 
will drive it to d, or a distance equal to that 
through which the first ball fell ; but it will 
itself rest at a, having given up all its own 
moving power to the second ball. 

If six ivory balls of equal weight 
be hung by threads of the same 
length, and the ball a be drawn out 
from the perpendicular, and then let 
fall against the second, that and the 
other four, c - d c /, will continue sta- 
tionary ; but the last ball b will fly 
b f e d, o off to B, being the same distance as 

that through which the first ball fell. Here the motion or rather the 
moving force of the ball a is propagated through the whole train to 
the ball b, which finding no resistance is acted on by the whole 
force. This experiment repeated with any number of balls would 




What cause modifies the operation of moving forces ? 

Illustrate the difference between the effects of elastic and inelastic 
bodies. 

What is the nature and cause of resiliency? 

How may its existence in ivory be made sensible ? 

Describe the experiments which illustrate the law of collision iu elas- 
tic bodies. 



VELOCITY OF MOTION. 25 

give the same result. It is proper to observe that in stating the 
effect of the collision of the balls in these experiments, they are 
supposed to be perfectly elastic bodies ; such however do not exist 
among- the substances with which we are acquainted ; the pheno- 
mena exhibited by ivory balls would therefore be nearly, but not 
exactly, such as are stated. 

20. The effect of elasticity in modifying the propagation of 
motion is curiously displayed in those exhibitions of human 
strength, which have occasionally taken place, and of which 
remarkable instances are related by some authors. Vopiscus, the 
Roman historian, mentions a circumstance of this kind, in his Life 
of Firmus, who, in the reign of Aurelian endeavoured to make 
himself emperor in Egypt, and who has therefore been reckoned 
one of the Thirty Tyrants. He was a native of Seleucia, in Syria, 
who espoused the cause of the famous Zenobia, Queen of Palmyra; 
and having been taken prisoner, he was executed by order of the 
emperor Aurelian. The historian says of Firmus, that he was 
able to bear an anvil on his breast, while others were hammering 
on it: he lying along, with his body in a curved position. And 
Beckmann, in his History of Inventions, notices the extraordinary 
feats of John Charles von Eckeberg, a German, who travelled 
over Europe about the beginning of the last century. After men- 
tioning other feats, he adds, " But what excited the greatest aston- 
ishment was, that he suffered large stones to be broken on hi? 
breast with a hammer, or a smith to forge iron on an anvil 
placed upon it."* A part of the mysterious effect produced in 
these cases is to be accounted for by the position of the exhibiter, 
which may be thus described. He must place himself with his 
shoulders resting on one chair, and his feet upon another, both 
chairs being fixed so as to yield firm support; and thus his backbone, 
thighs, and legs would form an arch, of which the chairs would be 
the abutments. The anvil also must be so large as by its inertia 
and elasticity, nearly to counterbalance the force of the hammer ; 
and thus the strokes would be scarcely or not at all felt ; besides 
which the elasticity of the man's body, as well as his position, 
would contribute to his security against the effect of the blows. 

Velocity of Moving Bodies. 

21. Communication of motion, however rapid, must take up 
some portion of time ; for as there can be no such thing as instan- 
taneous motion, much less can motion be propagated instantane- 
ously from one body to another. Hence motions performed with 

What property of matter is assumed in stating these experiments, 
and how is it lo be applied ? 

What remarkable example of the effect of elasticity does the human 
body afford ? 

What explanation can be given of the exploits of Firmus and Ecke 
berg ? 

* Hist, of Invent., Eng. Trans. 1797. Vol. iii. p. 20S. 

--C 



26 MECHANICS 

great velocity sometimes produce peculiar effects, as may be 
shown by the following experiments. 

EXPERIMENT I. 

22. A long hollow stalk or reed, suspended horizontally by two 
loops of single hairs, may, by a sharp quick stroke at a point 
nearly in the centre, between the hairs, be cut through, without 
breaking either of them. The hairs in this case would have been 
ruptured, if they had partaken of the force applied to the stalk ; 
but the division of the latter being effected before the impulse 
could be propagated to the hairs, they must consequently remain 
unbroken. 

EXPERIMENT II. 

23. A smart blow, with a slight wand, or hollow reed, on the 
edge of a beer-glass, would break the wand, without injuring the 
glass. 

EXPERIMENT III. 

24. A shilling, or any small piece of money, being laid upon a 
card placed over the mouth of a tumbler glass, and resting upon the 
rim of the glass, the card may be withdrawn with such speed and 
dexterity that the piece of money will not be removed laterally, 
but will drop into the glass. 

EXPERIMENT IV. 

25. A bullet discharged from a pistol, striking the panel of a 
door half open, will pass through the board, without moving the 
door; for the velocity of the bullet will be so great that the aper- 
ture is completed in a space of time too limited to admit of the 
momentum of the moving body being communicated to the sub- 
stance against which it is impelled. ? 

26. It is an effect of the principle just illustrated, that the iron 
head of a hammer may be driven down on its wooden handle, 
by striking the opposite end of the handle against any hard sub- 
stance with force and speed. In this very simple operation, more 
easily conceived than described, the motion is propagated so sud- 
denly through the wood that it is over before it can reach the iron 
head, which therefore, by its own weight, sinks lower on the han- 
dle at every blow, which drives the latter up. 

27. The velocity of motion is measured by time and space 
taken conjointly or relatively. Thus, a body moving through a 
given space, in a certain time, and supposed to pass through 
every part of that space at a uniform rate, is said to move with a 
velocity denoted by the ratio of the time to the space ; and there- 
State the four experiments which exemplify the peculiar effects ot 

rapidly communicated motions. 

How do you explain the operation of driving a handle into the eye of 
a hammer ? 

How is velocity of motion measured ? 

How are the relative velocities of different bodies estimated ? 



KINDS OF MOTION. 27 

fore a uniformly moving body will describe equal spaces in equal 
times, and different bodies relative spaces in relative times. 
Hence a horse that will trot eight miles in an hour, would trot ^ 
sixteen miles in two hours, and twenty-four miles in three hours, ' 
if he could traverse the distance with unabated speed. If in this 
case the three distances mentioned be considered as three distinct 
journeys, it will readily be perceived that the horse must have 
passed through the same distance, in each of the two hours of the 
second journey, and each of the three hours of the third journey, 
as in the single hour of the first; and this is what is meant by the 
statement that equal spaces are passed over in equal times ; so that 
when the distance travelled is doubled or tripled, the time wil] 
be doubled or tripled also ; and if the distance is reduced to one- 
half or one-fourth, the time will be reduced in the same propor- 
tion. The relative velocities of different bodies must be estimated 
in a similar manner. A man walking three miles in an hour would 
require double the time to perform a journey of eighteen miles, 
that would be taken up by another man running six miles an 
hour ; and a horse galloping twelve miles an hour would complete 
the journey in one-fourth of the time of the first man, and one- 
half the time of the second man. The minute-hand of a com- 
mon clock or watch has twelve times the velocity of the hour-hand, 
since the former passes through a whole circle, while the latter 
is passing through the twelfth part of it. 

27. The velocity of a uniformly moving body may be disco- 
vered by dividing the space passed through by the time consum-* 
ed: thus, the velocity of a steam-boat, going eighteen miles in > 
two hours, will be found to be nine miles an hour. The velocity'' 
being known, the distance passed over in a given time may be 
discovered, by the contrary operation of multiply ing the velocity by 
the time : thus, the steam-boat, with a velocity of nine miles an 
hour, will of course run twice nine miles in two hours, and forty- 
eight times nine miles in forty-eight hours. 

Different Kinds of Motion. 

28. Motion may be uniform or variable with respect to its rate 
or relative velocity. The nature of uniform motion has been just 
pointed out: and that of variable motion will be subsequently 
investigated. But motion may be different in one case from what 
it is in others, when considered with regard to the manner in 
which a body moves : as whether in a straight line, in a circle, 
or in any other curve. The line described by a body, in passing 
from one point to another, is called its direction, or line of motion. 
The direction of a moving body may be either a right line, across 
a level surface, or plane ; a curved line, passing over a similar 
plane ; or a curved line, the different parts of which are not on 
one plane. 

What is the method of discovering the velocity of a uniformly moving 
body ? of computing its distance passed over ? 
Whllt distinctions of motion are founded on its direction? 



28 MECHANICS. 

29. Curvilinear motion is of a more complicated nature than 
motion in a straight line, the circumstances relating to it therefore 
cannot be properly explained without a previous investigation of 
rectilinear motion. 

Sir Isaac Newton, in his great work entitled " Principia Phi- 
losophic Naturalis," " Principles of Natural Philosophy," has 
laid down three general positions, styled Laws of Motion, which 
have been considered as the foundation of mechanical science. 
These laws are the following: 

i. 
" Every body must continue in its state of rest, or of uniform 
motion in "a straight line, unless it is compelled to alter its state 
of rest or motion, by some force or forces impressed upon it." 

ii. 
" Every change of motion must be proportioned to the impress- 
ed force or forces, and must be in the direction of that force." 

in. 
"Action and reaction are always equal and contrary to each other." 

30. Both the first and the last of these laws or positions, relat- 
ing to moving bodies, have been already discussed, and their conse- 
quences pointed out: they may therefore be admitted as propo- 
sitions not requiring further demonstration. 

The second law of motion is of the highest importance, as it re- 
lates to compound motion, and the direction of a body acted on by 
two forces in different but not contrary directions. The effect of 
forces thus applied will be most readily understood after a short 
explanation of the nature of reflected motion, which affords a 
familiar example of action and reaction, the subject of the third of 
the preceding laws. 

31. If a cricket-ball, or any similarly shaped elastic body, be 
dropped perpendicularly on a smooth pavement, it will rebound to 
a certain point in the same straight line in which it descended ; 
but if it be impelled obliquely against the pavement, it will not 
rise in a perpendicular line, but in a line having the same degree 
of obliquity as that in which it struck the pavement. 

Thus, if the ball were dropped from a, to the 

pavement at b, its upward course would be in 

the same line, b a,- but if it be thrown in the 

line c b, it will rebound in the line b d. In this 

case the angle formed by the line c b, with the 

line a b, is called the " angle of incidence," and 

that formed by the line d b, with the line a Z>, 

il!i|llMII»ll;ill|l!i;::^;V:,:';^ « the angle of reflection ;" and it is to be observ- 

& ed that these angles will always be precisely 

equal. For it signifies not whether the obliquity of the line of 

incidence be great or small, since the line of reflection will in every 

What three laws of motion were laid down by Newton ? Which of 
these is of the greatest importance, and why ? 

How is the principle of compound and reflected motion illustrated in 
the motions of cricket and billiard balls ? 




EQUILIBRIUM. 



29 




case have the same obliquity, and consequently form a similar an- 
gle with the surface from which the body rebounds. 

32. Suppose the parallelogram in the 
margin to represent a billiard-table, if a 
ball standing on it be impelled in the di- 
rection a b, it will strike against the end 
cushion and return in the line b c, and 
either of those lines would form a similar 
and very acute angle with a line drawn 
between them parallel to the sides of the table ; but if the ball 
were driven from a against the side cushion at d, it would return 
m the corresponding line d e. 

33. Equal weights, or equal forces of any kind, acting on a 
body, in a similar manner, but in opposite directions, will keep it 
in a state of rest or equilibrium, like the scales of a common 
balance, each loaded with a weight of one pound. But when the 
arms of a balance are of unequal lengths, as in the steelyard, a 
small weight fixed at the end of the longest arm will counter- 
poise a much greater weight at the end of the short arm. 

„ 34. Let a represent a 

9 globe of lead resting on a 
level surface, and having 
an iron rod passing exactly 
through its centre, the ex- 
tremities of which e and/ 
are equidistant from the 
ball ; if threads of equal 
lengths be fixed at those points with hooks at the lower ends for 
the suspension of weights, the globe and rod will be kept in equi- 
librium so long as the weights b and c are equal ; but if a longer 
rod be passed through the ball projecting further from it towards 
g than towards e, a smaller weight d will then counterbalance the 
weight 5, and the relative number of ounces or pounds contained 
in thew weights will always bear certain proportions to the num- 
ber of inches or feet in the respective parts of the rod ef, and eg. 
Here the equilibrium is maintained by equal forces acting in 
opposite directions; and the illustration of this simple principle is 
deserving of attention, as it leads to the consideration of the case 
of equilibrium maintained by the application of three forces. 

35. In the annexed figure the weight a 
being attached to the centre of a cord passing 
over two small wheels, and the weights b 
and c to either end of the cord, the equilibri- 
um will be maintained only while the central 
weight counterbalances those at the ends, 
in order to which, exclusive of the effect of 



r 




How may the equilibrium of a body be preserved, and how is this 
subject exemplified ? 

How may an equilibrium be maintained by the application of three 
forces to a flexible cord ? 

c 2 



30 MECHANICS. 

friction, the weight a must be less than the sum of the two equal 
weights b and c taken together. For if the weight a be equal to 
the sum of b and c, there can be an equilibrium only when the 
two ends of the cord which sustain it become perfectly parallel 
to each other and to the parts which support b and c. This case 
is familiarly illustrated by the manner often adopted of suspend- 
ing lamps from ceilings by means of a weight, to which the two 
ends of a chain or cord are attached, which having passed over 
two puilies at the ceiling very near each other, comes down 
through a hole in the centre of the weight, and receives the lamp 
at the middle part of the chain. By this means free motion is 
allowed to the lamp to ascend and descend through a convenient 
distance, and the equilibrium is maintained in all positions. If 
the weight a be greater than the sum of b and c the cord will ob- 
viously sink in the centre, and the weight b and c be drawn up to 
the wheels ; and weight added on either side will drag down the 
cord on the side of the additional load and raise the central and 
opposite side-weight. 

f. 36. Suppose a cord, as in the marginal 

_; figure, stretched over the wheels E F, at- 

tached to an upright board, and having fixed 
to its extremities the weights B C. From 
any part of the cord, between the wheels, as 
at H, let a weight A be suspended, it will 
then draw down the cord so as to form an 
angle, E H F, and the weights will remain 
in equilibrium. It is obvious that in this 
case the weight A, acting in the direction 
H A, will counterbalance the weights B and C, acting in the 
direction H E and H F, and their joint forces must be equivalent 
to a force equal to A, acting in the direction H G. To ascertain 
the relative effect of the weights thus operating, it will be neces- 
sary to complete the figure, by drawing on the board the dotted line 
H G, in the direction of the cord A H ; and lines under the cords H E 
and H F. Then on the line H G mark the point a, and H a must 
be supposed to represent as many inches as the number of ounces 
contained in the weight A. From a draw the dotted line a i, 
parallel to H F, and the dotted line a c, parallel to H E ; then if 
the diagram were in the proportion just described, the line H b 
would contain as many inches as there were ounces in the weight 
B ; and the line H c as many inches as the number of ounces in the 
weight C. A moment's reflection will show that the relative 
weights and lengths might consist of any denominations of weight 
and longitudinal measure ; so that feet and pounds, or any greater 
or smaUer denominations might have been substituted for inches 
and ounces ; only in every case the same denomination of longi- 



What familiar illustration can be given of an equilibrium of this 
»ort r 
Describe the apparatus for exemplifying the parallelogram of forces. 




PARALLELOGRAM OF FORCES. 31 

mdinal measure must be applied to all the lines, and the same 
denomination of weight to all the gravitating' forces.* 

37. The case just considered affords an experimental illustration 
of what is called the parallelogram of forces, a principle of the 
utmost importance in mechanics, since it enables us to estimate 
the joint operation of moving powers, as well as their relative 
effect or influence. 

In the preceding diagram, the parallelogram of forces is repre- 
sented by the lines a b,b H,H c, and c a, and the line Ha, joining 
the opposite angles, which is called the diagonal. The sides of 
the parallelogram, a b, and a c, will represent the quantity and direc- 
tion of the two forces acting together, and the diagonal H a will 
denote the equivalent or counterbalancing force. This last force is 
styled the resultant, and the two forces opposed to it are its com- 
ponents. 

38. In the preceding examples, the object has been to show the 
effect of opposing forces in producing equilibrium ; but precisely 
the same method may be taken to explain the operation of forces 
applied in different directions, when their effect is to produce mo- 
tion, instead of restraining it. 

If a body A be impelled at the same time 
by two forces, which would separately cause it 
to describe the lines A B and A C of the paral- 
lelogram A B D C, the body will, by their joint 
action, describe in the same time the diagonal 
A D. For if the body had been previously 
moving with the velocity, and in the direction A B, and had been 
acted on at A by the force A C, it would have described A D in 
the same time. So that, whether the forces begin to act simulta- 
neously or successively, their effects may be calculated on simi- 
lar principles. 

a^__ B 39. When the angle at which 

the different forces meet is very 
acute,they act with greater power on 
21 the moving body ; thus, as the angle 
C A B, made by the directions of the composing forces, decreases, 
the effect arising from their joint impression will be increased ; 

Whence does this principle derive its importance in mechanics ? 

How is the parallelogram of forces applied to explain the laws of mo- 
tion ? 

Under what circumstances will the effects of two forces co-operate in 
producing motion in the same direction ? How may they destroy each 
Jther's effects ? 



* On this subject, see a description, in the Journal of the Franklin 
Institute, vol. 3. p. 354, of the tricardo, showing under what circum- 
stances three forces may produce a stable, and in what cases an unstable, 
equilibrium. — Ed. 





32 MECHANICS. 

and hence the diagonal A D, which expresses that effect, will 
likewise be increased. Therefore, when the angle CAB van- 
ishes, or in other words, when the sides A C and A B coincide 
with the diagonal, the joint forces will have their full effect; but 
this would no longer be a case of the composition of forces, but 
of the junction or union of two forces. 

40. When the angle B A C, made by 
the directions of the two forces, is very- 
obtuse, their effect is diminished, and 
the diagonal, representing the resultant 
of the forces, is consequently contracted. 
It will be obvious, therefore, that when the sides A B and A C 
meet without forming any angle, the forces will act in opposite 
directions ; and provided they were equal forces they would de- 
stroy each other, no motion taking place ; but if one force be su- 
perior to the other, the body will move on, not in a diagonal line, 
but in the direction of the greater force. 

41. The combined effect of three or more forces acting on a 
body in different directions, may be discovered by means of 
the parallelogram of forces ; and a single force may be thus as- 
signed which will be the resultant of those forces. This may be 
done by obtaining first the diagonal representing the resultant of 
the combination of two forces, and considering that diagonal 
as the side of a parallelogram, of which a line representing a 
third force will form one of the other sides, and the parallelogram 
being completed, the diagonal will be the resultant of the first 
three forces ; and the operation may be extended in the same man- 
ner, so as to discover the ultimate resultant of any given number 
of forces. 

Let the point A be impelled by 
forces in the directions A B, A C, 
A D, and A E ; then, to find out the 
resultant of these combined forces, 
complete the parallelogram C A B F, 
and the diagonal A F will exhibit the 
result of the forces, A B and A C. 
Complete the parallelogram D A F G, 
and its diagonal A G will denote the 
E^ result of the three forces A B, AC, 

and AD. In the same manner, complete the parallelogram E A 
G H, and the diagonal A H will represent the force compounded 
of all the four forces, A B, A C, A D, and A E. But the con- 
struction may be simplified by merely drawing the lines B F, 
equal and parallel to A C ; F G, corresponding with A D ; and 
G H, bearing the same relation to A E ; then, the line joining A 
and H, which as before will express the resulting force. 

How may the combined effect of several forces be determined ? Con- 
struct and explain the diagram relating to this subject. 




COMPOSITION OF FORCES. 



33 




42. It may be demonstrat- 
ed by means of the parallelo- 
gram of forces, that from 
three forces acting- in the 
F directions A B, A C, and A 
D, in the proportions of the 
length, breadth and depth of 
a parallelopiped,* will result 
a motion in the diagonal A F of that parallelopiped; for A B and 
A C compose A E and A E and A D compose A F ; which last 
is the resultant of the moving forces in the directions of the three 
sides of the parallelopiped. 

th Th j.^f ect of , the com P osi tion of forces, when a body im- 
pelled in different directions takes its course in a diagonal line 

exerted 6 - ^ impelUng f ° rCeS ' m ^ be thus experimentally 

On a billiard-table, A B C D, 
place a ball at G, equally distant 
from the side B C, and the end 
C D, then let two spring guns, 
capable of communicating equal 
impulses, be placed so that when 
the ball is impelled by E, it will 
move along the side A D, and 
1> that when the ball is impelled by 
F only, it will move in the line 
G H : then if the ball be struck 
by both the guns at the same instant, it will be found to move in 
the diagonal line G C, in the same time in which it would have 
moved from G to D, impelled by the gun E alone ; or from G to 
H, if acted on only by the gun F. From the observations which 
have been already made on the relations between the extent of the 
lines described by moving bodies, and the amount of the forces 
by which they are impelled, it will be apparent that this experi- 
ment may be so modified as to show what would be the direction 
01 the ball, when the impelling forces, or the angles at which thev 
acted, were variously adjusted. J 

44. The operation of the principle called the composition of 
forces may be perceived in numerous cases of frequent occurrence 
Indeed there are no motions with which we are acquainted that 
can be considered, strictly speaking, as instances of simple mo- 
tion ; for the effects of gravitation and the diurnal motion of the 
earth are alone sufficient to occasion some degree of complexity 

What will be the direction and amount of a motion produced by three 
forces proportionate to the length, breadth, and depth of a parallelo- 

What experimental illustration exemplifies the composition of forces 3 
How extensive is the application of this principle ? 




* See Introduction, 5. 



34 MECHANICS. 

in all motions taking place on the earth's surface. Simple motion 
therefore is only relative. . 

45. Suppose two persons to be seated on the opposite sides ot 
an omnibus, or any other oblong carriage, and to pass a ball for- 
wards and backwards, from one to the other, in a level line. 
Now, if the carriage were four feet wide, and the ball were passed 
across that space in precisely the same time that the carriage 
would be going four feet along an even road, the real motion ot 
the ball through the air would be in a zigzag line. 

46. A stone dropped on the deck, from the mast-head of a ship 
under sail, would be affected by the motion of the vessel, as well 
as by the force of gravitation, and would therefore fall, not m a 
perpendicular, but in a diagonal line. 

r< -va Let A represent the mast, C the stone, D the 
1 deck, and the line C E will be the distance that the 
I mast-head will have moved, while the stone would 
\ « have fallen, by the force of gravity alone, from C to 
\ jl the point under it on the deck ; the mast being fixed 
\ f: is carried forward by the ship, and therefore the 
\ f: foot of the mast will have moved equally with the 
\g head, and will have reached the point vertically be- 
\'l neath E when the stone touches the deck; the stone 
i\ will also be found at the foot of the mast, having 
»k taken a diagonal direction, in consequence of its 
- p being impelled at the same time by the ship's mo- 

tion and by its own weight. For, if it had not been affected by 
the former as well as the latter, it would have fallen where the 
foot of the mast was when it began to fall, and not at the actual 
foot of the mast. . 

47 Any one who has witnessed the common feats ot equestrian 
exhibiters at a circus, or elsewhere, may have seen a man leap 
from the back of a horse over a garter or handkerchief stretched 
horizontally across the track in which the horse was galloping, 
round the border of a circular area, and the horse passing under 
the garter, the man comes down again 
on the saddle, after finishing his leap. 
To do this, it is only necessary for the 
rider to spring upright from the sad- 
dle, on which he was previously stand- 
_ incr, and suffer himself to sink by his 
own weight on the saddle ag°ain; for as his body ^would partake 
of the motion of the horse, that force would be efficient to carry 
nim forwards, and his motion in rising, by an impulse wh ch 
would carry him from A to B if the horse were standing still, 

" What is the real motion communicated to a body thrown from one 

k\c\p of n carriflo-e to another when in motion ?..-.. , 

IlluLateS principle in .he falling of a body from the mast-head 

° WnarlT/erriaLtrian performer, after leaping opwdfroma 

horse in motion, to alight again on the saddle ? 





RESOLUTION OF FORCES. 35 

would be nearly in the line E, while he would descend in the 
corresponding- line F, through the joint effect of the force derived 
from the horse, and his own weight, the latter of which alone 
would occasion him to sink in the direction C D, or G H. 

48. As it has been observed that all motions are really of a 
compound nature, resulting in a greater or less degree from com- 
bined forces, it may sometimes be requisite to ascertain the sepa- 
rate effects of acting forces ; or to determine what portion of any 
given force acts in some direction different from that in which 
motion takes place. The operation requisite for this purpose is 
called the resolution of forces, the object not being as before, to 
discover the resultant from the combining forces, out to discover 
one or both of those forces from the resultant. 

£_ If a compound force, acting upon a body, pro- 
duces motion in the direction A B, and it is re- 
quired to find the part of that force which affects 
this body in any other direction, as D C ; by 
drawing A D perpendicular to the direction D C, 
will be found the proportion which the absolute 
force bears to that part, which acting alone would produce mo- 
tion in the proposed direction. 

49. A boat may be moved across a river by the current passing 
in a direction parallel to its banks. To effect this the boat must 
have a rope fastened to it- the other end of which is connected 
with another rope extended directly across the stream, a noose or 
ring being fixed to the first or boat-rope, through which the 
stretched rope is passed in such a manner that the ring may slide 
freely in either direction. Then the rudder of the boat being pro- 
perly turned to receive the impulse of the current, it will pass 
across the river, for the ropes will prevent it from being carried 
down the stream, while it glides with ease transversely as the 
ring of the boat-rope slides from one extremity to the other of the 
extended rope. Part of the force of the current in this case is 
destroyed, and the remainder is made to produce a motion in a 
direction different from that in which the water is flowing. The 
velocity of the current and that of the boat being ascertained, it 
would be easy to calculate what proportion of the moving force 
acted on the boat. 

50. When the impulse of air or water is employed as a moving 
power, either can seldom act directly and with full force, some 
portion being lost, and the effect consequently diminished. A ship 
sailing with a side wind has the sails set obliquely with respect 

By what operation may the separate effects of acting- forces be ascer- 
tained ? 

What is the precise object to be discovered in this case? construct and 
explain the diagram. 

How is the resolution of forces applied in the rope ferry ? How might 
we calculate what proportion of the moving force acted on the boat ? 

What examples are afforded in which the impulse of air and of water 
produces a resolution of forces ? What becomes of the ineffective part 
of the force in these instances ? 



36 MECHANICS. 

to the course pursued ; so the vanes of a windmill, and the float- 
boards of an undershot water-wheel are moved in general by a 
force applied in a slanting direction. Indeed the motion of a 
windmill would be prevented, by setting the surface of the sails 
perpendicular to the direction of the wind. In these and many 
other cases, only part of a moving force is brought into action, the 
other part being dissipated and lost, because it cannot be made to 
act in the required direction. 

Gravitation. 

51. Among the causes of motion, or moving forces, there are 
some, the effects of which are simple and uniform, producing move- 
ment in a single direction or straight line, and for a given time, 
proportioned to the degree of impulse. Others act in more than 
one direction, but with combined effect, so as still to produce 
uniform motion. Nature, however, presents to our notice motions 
which are not uniform, the velocity of the moving body varying 
in different parts of its course, so that the velocity or rate of motion 
may gradually increase to a certain point, and be suddenly termi- 
nated ; or first increase, and then decrease till it ceases altogether. 
Motion with a perpetually increasing velocity is called accelerated 
motion. The phenomena of simple and compound rectilineal mo- 
tions have been already described ; but those of accelerated motion, 
which come next to be considered, cannot be fully understood 
without a previous acquaintance with the laws of gravitation, with 
which they are intimately connected. So general indeed is the 
erTect of the property of gravity or weight on all bodies, within the 
reach of our observation, that its influence is perpetually interfering 
with our operations and experiments ; and hence references have 
necessarily been made to it in the preceding pages, as in explain- 
ing the cause of the decay of motion, and elsewhere ; but it will be 
requisite here to take a more extensive view of the nature and 
effects of this important principle. 

52. Gravitation or Gravity has been noticed in the Introduction, 
under the appellation of gravitative attraction, as distinguished 
from cohesive attraction, capillary attraction, magnetic attraction, 
and other forces which tend to bring bodies into contact. Most of 
these forces or kinds of attraction are perceived only under par- 
ticular circumstances ; as cohesive attraction, which seems to act 
on solid and liquid substances alone, and not on gases ; and capil- 
lary attraction, which only takes place between certain fluids and 
solids. But the attraction of gravitation differs from other attrac- 
tive forces in being a common property of all bodies, since every 
thing to which we can attach the idea of materiality is affected 
more or less by gravitation. 

53. It is by no means inconsistent with this statement that some 

What is the distinctive character of variable motion ? What is acce- 
lerated motion ? 

How is gravitation distinguished from other species of attraction? 
How extensive is its influence over material things ? 



GRAVITATION 37 

bodies, possessing all the characteristics of solid matter, capable of 
being seen and felt, yet in certain circumstances, instead of exhi- 
biting' the common effect of gravity, in falling towards the earth 
or pressing on it, display the contrar3 r phenomenon of ascending 
from it. Thus, smoke will be seen, in some states of the atmo- 
sphere, rising in a column to a considerable height. Even solid 
masses of no small bulk and weight may be made to ascend to a 
great height, as by means of an air-balloon. But all these and 
similar phenomena are in fact so many instances of the effect of 
gravitation; for the ascending bodies are driven upward solely by 
the force of the medium through which they pass; since the parti- 
cles of smoke, or the balloon with its car and contents, cannot 
advance upward in the most minute degree without displacing, 
or thrusting downward, portions of the atmosphere equal to their 
own bulk. Hence it will be perceived that aerostatical bodies 
do not ascend because they possess absolute levity, but simply 
because, bulk for bulk, they are lighter than the air. A cork or a 
piece of deal, for the same reason, will float on water, and if 
pressed down in it will rise again to the surface, by the effect of 
relative levity. 

54. All substances, then, gravitate towards the earth ; that is, 
they have weight, which occasions them to fall to the earth when 
dropped from a height above it; to rest upon it with a certain 
degree of pressure, according to circumstances ; or if rendered 
buoyant, to rise in the atmosphere surrounding the earth, till they 
reach a part of it where it is less dense than near the surface, so 
that a portion of it, precisely equal to their bulk, would exactly 
counterpoise them, and there of course they could neither rise nor 
fall, without an alteration of their own weight taking place. In 
the case of an air-balloon, the aeronauts have the means for les- 
sening its buoyancy whenever they may find it convenient, by 
opening a valve, and letting out a part of the gas, or light air, 
to which it owes its ascending force ; thus they can, at any time, 
render the weight of the whole apparatus much greater than 
that of an equal bulk of atmospheric air, and then it must fall to 
the ground. Smoke only remains suspended till its particles 
unite, and thus becoming heavier than the air, they descend in 
the form of small flakes of soot, covering with a dingy coat or 
incrustation all buildings, after a time, in large and populous 
places. 

55. Let us suppose for a moment that while a mass of smoke 
and an air-balloon were hovering in the air near together, and at 

How is the universal prevalence of gravitation to be reconciled with 
the appearance of light substances rising from the surface of the earth p 
What is the true explanation of these phenomena ? 

What expedient enables the aeronaut to descend from a higher to a 
lower level in the air ? 

In what manner is smoke finally deposited from the air ? 

What would be the effect on suddenly removing the air from beneath 
a mass of smoke and an air-balloon hovering uear each other ? 

D 



38 



MECHANICS. 



m\ 



®0 



precisely the same height, it were possible to withdraw from 
under them the support of the atmosphere, it will be immediately 
perceived that they must fall ; but probably the young reader will 
be surprised to learn, that they would not only fall, but likewise 
that they would both fall through the same space in the same time ; 
so that if their common height had been five hundred feet, the 
smoke would have reached the surface of the earth at the same 
instant with the balloon, though the latter might in weight far 
exceed the other body. It must not be imagined that the cir- 
cumstance just stated is a mere philosophical conjecture, or that it 
cannot be confirmed by the test of experiment ; for, though it is 
impossible to annihilate the atmosphere, or effectually remove it 
from beneath an air-balloon, or any other body suspended in it, yet 
on a small scale appearances precisely similar to those just de- 
scribed may be easily exhibited. 

CJ 56. Let A represent a tall bell-glass, 

open at the bottom, and having the top 
closed, so as to be air-tight, by a brass 
cap or cover, B, through which passes the 
wire C, fitting close, but capable of being 
turned without admitting the air. The 
lower end of the wire must be made to 
support a small stage, the two sides of 
which, D D, will fall and separate, when 
the wire is turned in a transverse direc- 
tion. Then, the stage being fixed, a gold 
coin and a feather, E and F, or any 
two small bodies differing greatly in their 
comparative weight, may be laid on the 
stage, and the bell-glass, or as it is called, 
receiver, being placed on the plate, G, of an air-pump, must be 
exhausted of the air it contained. This being done, if the two 
bodies E and F are made to fall by turning the wire, it will inva- 
riably be found that they will both strike the plate of the air- 
pump beneath them at the same point of time. 

57. The influence of gravitation is not only extended to all bo- 
dies on or near the surface of the earth, but likewise, as we have 
the utmost reason to believe, to all bodies in the universe. This is 
not the proper place to describe the nature and operation of those 
forces which regulate the orbits of the moon, the planets, and the 
comets belonging to the solar system ; but it may be here observ- 
ed that Sir Isaac Newton discovered gravity to be the cause of all 
the motions of the heavenly bodies ; and that the laws of gravita- 
tion displayed in the monthly revolution of the Moon round the 
Earth, the annual circuit of the Earth round the Sun, and the 

In what manner can we prove, experimental]}', that light and heavy 
bodies would fall with equal velocity if the air were suddenly annihi- 
lated ? 

How extensively is gravitation applicable to the works nf nature ? 

What discovery did Sir Isaac Newton make on this subject ? 



GRAVITATIVE ATTRACTION OF MASSES. 39 

corresponding motions of the other planets and their satellites are 
capable of the strictest mathematical demonstration. 

58. Gravitative attraction acts upon all bodies, with forces pro- 
pcrtioned to their masses. Thus suppose two bodies so situated 
as to be wholly exempt from the influence of any attraction except 
that resulting from their gravitation towards each other, they will 
then approach with velocities corresponding with their respective 
forces. If the larger of the two bodies be double the size of the 
smaller, the former will act with twice the force of the latter ; and 
therefore while the small body will move two feet in consequence 
of the double power of the larger one, the larger will move but 
one foot drawn by the single power of the smaller. If the larger 
body be four times the size of the other it will exert four times 
as much attractive force, or make the smaller body move with 
four times as great velocity as it would if the masses of the bo- 
dies were equal. 

59. Hence it may be regarded as a general law of gravitation, 
that while the distance between two bodies remains unaltered, 
they will attract and be attracted by each other, in proportion to 
their respective masses ; and therefore any increase or decrease 
of the mass must occasion a corresponding increase or decrease of 
the amount of attractive force, as measured by the velocity. 

60. Since gravitative attraction is a common property of all 
bodies, it may naturally be inquired why all bodies not fastened 
to the earth's surface do not, by their mutual attraction, come in 
contact ; or by what means the force which they derive from gra- 
vitation is prevented from appearing in their relations to each 
other. A little reflection will show that the cause of this seeming 
inactivity of bodies at rest is the overpowering influence of the 
earth's attraction. If a small particle of matter were placed at 
the surface of a solid sphere or globe of gold, one foot in diame- 
ter, its gravitation to the earth would be more than ten millions 
of times greater than its gravitation to the gold. For the diame- 
ter of the earth is nearly forty millions of feet, and the density of 
gold is nearly four times the medium density of the earth ; there- 
fore in a second, the particle would approach the gold less than 
the ten millioneth part of sixteen feet, a space utterly impercepti- 
ble. It is also owing to the immense difference in the mass of 
the earth and that of any one body on its surface, that the attrac- 
tive influence of bodies falling towards the earth produces an 
effect in drawing the earth upwards so insignificant as to be infi- 
nitely beyond the reach of our observation. 

61. Though we cannot institute direct investigations of the 

In what proportion does gravitation affect different bodies ? 

What would be the relative velocities of two unequal bodies actuated 
solely by each others gravitative attraction ? State the general law on 
this subject. 

Why do not all unconfined bodies rush together by their mutual at- 
traction ? 

Why do not falling bodies draw up the earth instead of descending to 
its surface ? 



40 



MECHANICS. 



comparative effect of gravitation, by making experiments on de- 
tached masses whose magnitude bears any considerable propor- 
tion to that of the earth, yet it may be shown that partially iso- 
lated portions of the earth's surface exhibit a sensible degree of 
gravitative attraction, when small bodies are brought near them. 
A mountain two miles in height and of an hemispherical figure, 
rising in a level country, would cause a plummet suspended be- 
side it to deviate one minute of a degree from the perpendicular 
direction which gravitation towards the earth would otherwise 
produce. Observations of this nature have been actually made 
on more than one occasion. The French Academicians, Bouguer, 
De la Condamine, and others, when employed in measuring a 
degree of the meridian, in Peru, towards the middle of the last 
century, having placed their observatories on the north and south 
sides of the vast mountain of Chimborazo, found that the plum- 
mets of their quadrants were deflected towards the mountain. The 
manner in which these philosophers ascertained the amount of 
die deflection of their plummets may be thus concisely explained. 

Their object being to determine 
the zenith distance of a star, I, it 
was necessary to regulate the posi- 
tion of a telescope by means of a 
quadrant, the plummet of which, in- 
stead of hanging in the vertical 
lines A F, and C H, on the oppo- 
site sides of the mountain, were 
found to take the positions A B, 
and C D, and thus the star seemed 
to have the zenith distances e I, and 
g I, instead of E I, and G I, which 
it ought to have had : hence it is 
obvious that the plummet was 
drawn aside, by the attractive force 
of the mountain, from its proper 
direction perpendicular to the earth's 
surface, through a space capable of 
being estimated by the differences perceived in making observa- 
tions on the star I from the opposite sides of the attracting mass. 
62. The phenomena thus observed by the French philosophers 
having given rise to discussion among men of science in different 
countries, it was thought desirable to ascertain, by experiments 
made for that particular purpose, the validity of the cause assign- 
ed. King George III. therefore was induced to send the Astro- 
nomer Royal, Dr. Maskelyne, to Scotland, in 1772, to make 

How may a comparison be made between tbe whole mass of the earth 
and an isolated portion projecting above its general level ? 

Describe and illustrate the experiments which have been instituted on 
this subject. 

What amount of deviation did Dr. Maskelyne find in his plummet on 
the sides of Schehallien ? 




RAVITATIVE ATTRACTION OF MASSES. 



41 




similar experiments on the north and south sides of Schehallien, 
a lofty and solid mountain in Perthshire, well adapted for the 
purpose. The deviation towards the mountain on each side, was 
found, after the most accurate observations, to exceed seven se- 
conds ; thus confirming the inferences of preceding- observers, and 
proving the universal operation of gravitative attraction. 

63. The influence of general gravitation was also experiment- 
ally demonstrated in a different manner, by Mr. Henry Caven- 
dish, in 1788. 

Two small metallic balls, C and 

D, were fixed to the opposite ends 

of a very light deal rod, which 

was suspended horizontally, at its 

centre E, by a fine wire. This 

arm, after oscillating some time horizontally by the twisting and 

untwisting of the wire, came to rest in a certain position. Two 

great spherical masses, or globes of lead, A and B, were then 

brought into such a position, that the attraction of either globe 

would turn the rod C D on its centre E, in the same direction. 

By observing the extent of the space through which the end of 

the rod moved, and the times of the oscillations when the globes 

were withdrawn, the proportion was discovered between the 

effect of the elasticity of the wire, and the gravitation of the balls 

towards the leaden globes; and a medium of all the observations 

being taken, the experimentalist was enabled to ascertain not only 

the actual influence of gravitation on terrestrial bodies in general, 

but likewise its relative influence as depending on the density of 

the attracting body. 

64. As gravitative attraction draws bodies towards the centre 
of the attracting mass, it might be expected that bodies under the 
influence of gravitation would diverge somewhat from a line per- 
pendicular to an horizontal plane beneath them. 

This indeed is precisely what takes place ; 
and if we imagine a pair of scales, as in the 
marginal figure, to be formed in such a manner 
as to bear a certain proportion to a sphere to- 
wards the centre of which each scale was at- 
tracted, the effect would be obvious. But the 
magnitudes of any bodies which we can make 
the subjects of experiment are so extremely in- 
considerable when compared with that of the 
earth, as to render the deviation from the per- 
pendicular, in lines which are actually conver- 
gent, quite imperceptible. 

65. It must also be considered that though the grand and pre- 
ponderating force of gravitation is directed towards the centre 

Describe the method adopted by Cavendish to demonstrate the influ- 
ence of gravitation, and the mean density of the earth ? 

What are the directions in regard to a horizontal plane of two bodies 
remote from each other, and obeying the force of gravitation ? 
d2 




42 MECHANICS. 

(and all bodies, like those just mentioned, are attracted towards 
the earth's centre), yet every particle likewise has an attract- 
ive power, therefore the gravitation of bodies on the earth's 
surface is the effect of the attraction of its entire mass. Hence 
in the investigation of the phenomena of falling bodies, it may 
be assumed that all the particles of the same body are attracted 
in parallel directions, perpendicularly to an horizontal plane ; for 
the spaces through which bodies fall, while under our observa- 
tion, are not of sufficient extent to render it necessary that any 
allowance should be made for the effect of direct attraction to- 
wards the centre. 

66. The slightest observation will enable any one to ascertain 
that the force of a falling body increases in proportion to the 
height from which it has fallen. When bodies are precipitated 
from a great height, they will strike with violence against a re- 
sisting surface, or penetrate deeply into a yielding mass. Aero- 
lites or meteoric stones, which are heavy bodies, resembling iron 
ore, several of which have fallen at different periods, have some- 
times been found to sink deeply into the earth ; as was observed 
with regard to a meteoric stone, fifty-six pounds in weight, which 
fell in a ploughed field in Yorkshire, England, in 1795. 

67. Experiments serving to illustrate the effect of accelerated 
velocity on falling bodies may be made by observing the rebound 
of an elastic body, when dropped from different heights. A mar- 
ble or a cricket-ball successively suffered to fall on a pavement, 
from the respective heights of a foot, a yard, and double or treble 
that height, would rise higher and higher at each trial, according 
to the extent of the space through which it had fallen. More ex- 
act experiments might be instituted by forming three or four balls 
of soft wax or moist clay, exactly of equal weight, as one pound 
each, and. letting them drop from different heights on some smooth 
hard surface; when it would be perceived that each ball was 
indented or flattened, on the side on which it had fallen, more or 
less deeply in proportion to the extent of the space it had fallen 
through. 

68. Having thus ascertained that the velocity of a falling body, 
as denoted by its final force, is increased by the augmentation of the 
distance passed through, it becomes an interesting speculation to 
determine what are the relative degrees of velocity produced by 
given distances of descent. In other words, it is desirable to 
know whether a body falling through a space during two seconds, 
or two minutes, would fall as fast again in the second period as 

t did in the first, or three times as fast, ten times as fast, or in 

Whence results the gravitation of bodies on the earth's surface ? 

How does the force of falling bodies vary with the heights from which 
ihey fall ? 

Exemplify this in the case of aerolites. 

What familiar experiments with elastic and with soft bodies prove the 
relation between velocity and extent of fall ? 

What relation does the velocity of a falling body actually measure ? 



LAWS OF GRAVITATION. 43 

what other ratio of acceleration. This is obviously a question of the 
relation between time and space, for velocity is the measure of 
that relation. Now the motion produced by gravitative attraction 
is a continually increasing motion, so that a body under the influ- 
ence of gravitation will not fall through exactly the same space 
in any two consecutive periods of time, however inconsiderable. 
For if we could suppose a single second to be divided into a thou- 
sand parts, a falling body would pass through a greater space in 
the second thousandth part of the second, than in the first thou- 
sandth part, and so on in like manner throughout its course. How- 
ever, in order to find out the rate or ratio of the increasing velocity 
of falling bodies, it will be sufficient to know what is the distance 
passed through by a descending body in each succeeding second, 
minute, hour, or any other equal portion of the time of its whole 
descent. 

69. When we consider the various circumstances which inter- 
fere with the motion of falling. bodies, some arising from the re- 
sistance of the medium through which they pass, and other inci- 
dental sources of irregularity, others from the varying force of 
gravitation itself, at different distances from the centre of attrac- 
tion, it will be at once perceived that the inquiry before us is 
surrounded with difficulties. It is no wonder then that very con- 
fused and erroneous notions concerning this subject prevailed till 
a comparatively recent period. 

70. Aristotle, whose opinions were long regarded as indisputa- 
ble, states, in his philosophical writings, that if one body has ten 
limes the density of another, it will move with ten times the ve- 
locity ; and that both bodies being let fall together, the first will 
fall through ten times the space that the other will in the same time ; 
besides other erroneous doctrines, which were generally received 
till his theory was overturned by the discoveries of the celebrated 
Italian philosopher Galileo, towards the end of the sixteenth cen- 
tury. He showed that bodies, under the influence of gravitation 
alone, would fall through spaces as the squares of the times of de- 
scent: that is, that a body, which would fall through one inch in 
one instant, would fall through four inches in two instants, and nine 
inches in three instants ; for the square of any number is the pro- 
duct of that number multiplied by itself, so four is the square of 
two, nine the square of three, &c. The principle thus laid down 
by Galileo, though disputed by some later philosophers,* has not 

Will gravitation alone ever produce a uniform velocity of motion ? 
exemplify this point 

How may the rate of increasing velocity be determined ? 

What prevented the early philosophers from obtaining exact notions 
of this subject ? 

What was Aristotle's opinion on the subject of falling bodies? 



* The authority of Galileo was questioned, and different opinions were 
maintained by philosophers concerning the ratio of the acceleration ot 



44 MECHANICS 

only been triumphantly established as a positive law of nature, 
with regard to falling bodies, but, as ahead) 7- mentioned, it has 
been shown by Sir Isaac Newton that it is a general law of na- 
ture, extending to the motions of the celestial bodies composing 
the solar system. 

71. In order to apply this principle to the purpose of ascertain- 
ing the precise ratio of the accelerating velocity of falling bodies, 
it is necessary to fix on some measure c-f time as the unit from 
which calculations must commence, and to determine what space 
a body will fall through in that portion of time; and these data 
being furnished, the application may be readily explained. 

72. But before we proceed to the further consideration of the 
velocity of falling bodies, as the effect of a uniformly accelerating 
force, it will be proper to observe that it can only be thus strictly 
estimated Avith respect to bodies falling through limited spaces, 
as short distances from the surface of the earth, Where the inten- 
sity of the gravitating force may be regarded as continuing the 
same during the whole period of descent. For not only does the 
velocity of gravitating bodies in descent become accelerated as 
they approach the centre of attraction, but the intensity of the ac- 
celerating force is also continually increasing. And on the con- 
trary, the intensity of the force diminishes as the distance in- 
creases. Hence the velocity of a body falling from a great height, 
as fifty miles from the earth's surface, would increase in a smaller 
ratio at the beginning of its descent, and in a much greater ratio 
towards the end of its descent, than that of a body falling through 
only as many feet. 

73. The force of gravitalion is to be estimated by the same rule 
that has been already stated as applicable to the velocity of fall- 
ing bodies. It increases as the squares of the distances of bodies 
decrease, and decreases as the squares of their distances increase. 
Thus, if one body attracts another with a certain force at the dis- 
tance of one mile, it will attract with four times the force at half 
a mile, nine times tbe force at one-tbird of a mile, and so on in 
proportion ; and on the contrary, it will attract with but one-fourth 
the force at two miles, one-ninth the force at three miles, one-six- 
teenth of the force at four miles, and so on as the distance in- 
creases. Applying this principle to the gravitative attraction of 
the earth, it follows that its force must be four times greater at 
the earth's surface than at double that distance from its centre ; 

What truth in regard to gravitation was first established by Galileo ? 

What measure must we adopt previously to applying the principles of 
gravitation ? 

Does the rate of acceleration by gravity continue the same at all dis- 
tances above the surface ? State the law applicable to this subject. 

the velocity of falling bodies, even till the time of Newton's discoveries. 
— Vid. Regis Physic, lib. ii. cap. 23 ; also, Annotations of Dr. Samuel 
Clarke, on Rohault's Treatise on Natural Philosophy, a work which was 
considered as of standard authority in the beginning of the last centur) 



GRAVITATIVE ATTRACTION OF THE EARTH. 45 

and as the weight of bodies is estimated by the pressure or gravi 
tating force with which they tend towards the earth, a body 
weighing one pound at the earth's surface would have only one- 
fourth of that weight, if it could be removed as far from the sur- 
face of the earth as the surface is from the centre. And at the 
distance of the moon from the earth, which is 240,000 miles, the 
weight or gravitating force of the same body, as affected by the 
attraction of the earth, would be equal to only the 3600th part of 
a pound. For reckoning the distance of the earth's surface from 
its centre to be 4000 miles, that is, half its diameter,* the dis- 
tance of the moon would be sixty times as great, and the square 
of that number, or 3600, would, as just stated, indicate the de- 
crease of gravity, at the distance of 240,000 miles from the surface 
of the earth. 

74. This decrease of weight, in proportion to the squares of in- 
creasing distances, might in some situations be made the subject 
of experiment. A ball of iron, weighing a thousand pounds at 
the level of the sea, would be perceived to have lost two pounds 
of its weight, as ascertained by a spring balance, if taken to the 
top of a mountain four miles high. The same body removed 
from Edinburgh to the north pole would gain the addition of three 
pounds ; and if conveyed to the equator, it would suffer a loss of 
four pounds and a quarter. To account for the loss of weight in 
the last-mentioned situation, it must be recollected that the earth 
is not a perfect sphere, but that its figure is spheroidal, the diame- 
ter of the earth from pole to pole being somewhat less than in the 
line of the equator; the equatorial regions therefore must be more 
distant from the centre of attraction than the polar regions, and 
the force of gravitation at the former consequently less than at 
the latter. Hence the point of greatest attraction must be at 
either of the poles ; for if the iron ball, just mentioned, could be 
conveyed to the depth of four miles within the bowels of the earth, 
it would be found to be lighter by one pound than at the surface ; 
since it would be attracted on every side, and the force of gravi- 
tation upwards would in some degree counteract the preponderat- 
ing force with which it would press downwards. If it were pos- 
sible for the iron ball to reach the centre of the earth, it would 
necessarily there lose the whole of, its weight, for the attraction 
of gravitation acting equally in every direction, no effect would 

How much greater is the force of gravitation at the earth's surface, 
than at a semi-diameter above it ? How much would a pound weigh if 
carried to the distance of the moon ? 

How might the decrease of weight in bodies removed to a distance 
above the surface of the earth be experimentally proved ? 

How is difference of weights in different latitudes to be explained? 

What effect upon its weight would arise from carrying a body far be- 
neath the surface ? 

What would be the weight of a body carried to the centre of the earth ? 

* The mean semi-diameter of the earth may be estimated more ex- 
actly at 395G miles. 



40 MECHANICS. 

be produced, and the ball would be fixed, as if encircled by an 
infinite number of magnetic points. 

75. Connected with this part of the subject there are some cu- 
rious problems, the solution of which requires mathematical cal- 
culations, but the results alone are here introduced, as furnishing 
interesting illustrations of the power of gravitation. 

Suppose the axis of the earth were perforated from pole to pole : 
a bod} r falling through the perpendicular hole, being attracted on 
all sides, would be urged downwards only by a predominating 
force, proportional to its distance from the centre. The velocity 
acquired at this centre, reckoning the length of the axis 7900 
miles, would be equal to 25,834 feet each second. The time of 
descent would be 1268g seconds, or 21/ 8"g ; and the whole time 
of passing to the opposite pole 42' 16"^.* 

76. Conceive a body, under the mere influence of terrestrial 
attraction, to fall from the orbit of the moon to the earth's surface. 
At the mean distance of sixty semi-diameters of the earth from its 
surface, the initial force would be diminished 3600 times : with 
the same continued acceleration, therefore, it would consume a 
period of 526,578 seconds, or six days, two hours, sixteen minutes, 
and eighteen seconds, in performing the whole descent. The 
final velocity, on this supposition being 4680.69 feet each se- 
cond. Such would be the time of descent under the influence of 
uniform acceleration; but the time required with an acceleration 
inversely as the square of the distance from the centre would be 
only 414,645 seconds, or four days, nine hours, ten minutes, and 
forty-five seconds. And in this case the final velocity would be 
36,256.45 feet, or about seven miles each second. Abstract- 
ing, then, from the resistance of the atmosphere, a body propelled 
directly upwards, with this last velocity of 36,256.45 feet in 
a second, would mount to the orbit of the moon; but with the ad- 
dition of one hundred and twentieth part more, or 305 feet to every 
second, it would reach the sun; and with the further acceleration 
of less than one foot, amounting to 36,562.43 feet each second, the 
body would be enabled to continue its flight into the regions of 
boundless space. | 

What would be the velocity and the time of a body descending 
through a perpendicular hole along the axis to the earth's centre ? 
, How long Mould it take a body to fall from the moon to the earth ? 
and what would be its velocity on reaching the surface ? 

With what velocity must a body be shot upwards, in order to pass be- 
yond the solar system. 



* In the hypothetical case here propounded, it must be admitted that 
the acquired velocity of the body at the centre of the earth would over- 
come the obstacles to its ascent, and enable it to complete its passage. 

f Leslie's Elements of Natural Philosophy. 2nd edit. Edinb. 1829. 
Vol. i. p. 106, 7. 



ACCELERATED MOTION. 47 



Accelerated Motion. 

77. The increase or acceleration of velocity, from the force of 
gravitative attraction, has been stated to be as the squares of the 
numbers representing equal portions of the time during- which a 
bod)' falls. It has been found convenient to consider the time of 
descent of falling bodies as divided into seconds, so that if a body, 
under the influence of gravitation alone, falls one foot in one se- 
cond, it must fall four feet in two seconds, nine in three seconds, 
sixteeen in four seconds, and so on, in progression; the squares 
of the numbers of the seconds showing the number of feet passed 
through by the falling body at the end of each second. In order 
to discover the distance passed through in each particular second 
of the time, it is merely requisite to subtract, from the whole dis- 
tance completed at the end of that second, the number of feet at 
the end of the preceding second. Thus, from 4 feet, the distance 
in two seconds, take 1 foot, the distance in the first second, and 
3 the remainder, will be the number of feet passed through in the 
second second only ; from 9, the distance in three seconds, take 
4, the preceding distance in the first two seconds, and the remain- 
der 5 will be the distance in the third second; so from 16, the 
distance in four seconds, the preceding distance of 9 being sub- 
tracted, will leave 7, the distance in the fourth second. 

78. Gravitation being a continually acting force, a body falling 
through its influence alone would in every instant of jts descent 
move faster than in the preceding instant, and consequently, at 
the end of any given time, it would be impelled by a force be- 
yond that which carried it through the preceding space. This 
force may be estimated in the following manner. Suppose a body, 
after having fallen during one second, by the impulse of gravita- 
tion, to be no longer acted on by an accelerating force, but to con- 
tinue its motion with the velocity already acquired, describing 
through the remainder of its descent equal spaces in equal times. 
In such a case it would be found that the falling body, in every 
successive second of its descent, after the first, would pass 
through twice the space through which it had fallen in the first 
second by the force of gravitation. And the velocity being esti- 
mated by the space described uniformly in one second, it follows 
that the velocity acquired in one second must be equal to double 
the space through which a body w T ould fall freely by the action 
of gravity in one second. Since then th,e velocity increases in 
the same proportion as the time, it would be twice as great at the 
end of the second second, as at the end of the first, thrice as 
great at the end of the third second, and so on. 

How car, we discover the distance passed through in each separate 
second of the descent of a body ? Exemplify this by a particular case. 

With what uniform velocity per second would a body move, after hav- 
ing fallen for one second, supposing the force of gravitation to be then 
suspended ? 



48 



MECHANICS. 



Entire 


spa 


ce 




Velocity 


esti- 


Space in feet 


fallen th 


roi 


gli 




mated by 


feet, 


fall 


en through 


in feet at 


the 


end 




at the en 


d of 




in each 


of each second. 




each second. 




second. 


1 




. 


, 


2 


. 


. 


1 


4 




. 


# 


4 


. 


. 


3 


9 




. 


. 


6 


, 


, 


5 


16 




. 


. 


8 


. 


. 


7 


25 




. 


. 


10 


. 


. 


9 


36 




. 


. 


12 


. 


. 


11 


49 




. 


. 


14 


. 


. 


13 


64 




. 


. 


16 


. 


. 


15 


81 




. 


. 


18 


. 


. 


17 


100 




. 


. 


20 


. 


. 


19 



79. The following table, constructed on the supposition that a 
body would fall through one foot in the first second of its descent, 
as furnishing the most simple results, will afford some further il- 
lustrations of the positions laid down. 

Number of se- 
conds of the 
period of descent. 

1 

2 
3 
4 
5 

6 
7 
8 
9 
10 

80. It will at once appear from the inspection of this table that 
the time of descent of falling bodies increasing as the numbers 
1, 2, 3, &c, and the entire spaces passed through as the squares 
of those numbers, the augmentation of velocity will be repre- 
sented by the even numbers, in regular progression, and the spaces 
passed through in each second by the odd numbers. The sum 
of the number of feet in the fourth column will of course give 
the number of feet fallen through in the whole time ; and the dis- 
tance fallen through in any part of the time may be found in the 
same manner. Thus, 1 + 3 4-5, &c. to 19 inclusive will amount 
to 100. So the space fallen through in any number of seconds 
may be ascertained by adding the corresponding numbers in the 

second and third columns, toge- 
ther with the number representincr 
the space fallen through in the 
first second of descent. Thus 1 
+4=8 + 1=9; 12+36=48+1= 
49; 18 + 81=99 + 1=100. And 
the same results may be obtained 
in any similar cases. 

81. The nature of accelerating 
velocity, as exhibited in falling bo- 
dies, ma) r , perhaps, be somewhat 
! C elucidated by reference to the sp- 
ies of triangles in the annexed diagram. Let the line A B de- 
ote the time of the descent of a falling body, divided into equal 
portions, as seconds ; then the small numbered triangles may re- 
Explain the relation, as exhibited in the table, between the time, the 
entire space fallen through, acquired velocity, and space described in 
each second. What series of numbers represents the augmentation ol 
velocity ? 

In what geometrical figure may this relation be exhibited I 




LAWS OP ACCELERATED MOTION. 49 

present the space fallen through, under the influence of gravita- 
tion : the number of the triangles in each line showing the num- 
ber of feet passed through in each second, and the entire number 
the whole space described in five seconds. By completing the 
square, as with the dotted lines, it ma}*' be perceived how it hap- 
pens that the velocity, acquired by a falling body at the end of 
each second, is more than is expended in its passage through the 
next second ; and also it will appear that a body, moving uni- 
formly with the velocity acquired at the end cf any given second 
of time, will describe double the space described in the same 
time by a body falling under the influence of gravitation alone. 
For suppose the triangles c, b, c, d, e, to denote the surplus velo- 
city at the end of each second, which must be sufficient to cany 
the falling bod)^ through one foot, they will, if added successively 
to the numbered triangles in each line, show the velocity acquired 
in each succeeding second ; and therefore the triangles 17, 18, 19, 
20, 21, 22, 23, 24, 25, and e will be ten in number, the amount 
of the velocity acquired at the end of five seconds. Now a body 
moving with the uniform velocity of ten feet in a second would 
pass through the distance of fifty feet in five seconds; while a 
body falling through gravitation only would pass through but 
twenty-five feet in the same time : and the space described by the 
uniformly moving body, at the rate of ten feet in a second, may be 
represented by the square ABCD; while the triangle ABC 
would represent the space described by a bodjr moving with ac- 
celerated velocity, in the same time ; and as the square is equal 
to the doubled triangle, so the former space would be double the 
latter. 

82. Hence likewise a body moving uniformly, with half the 
velocity it would acquire at the end of any given time, would pass 
through a space exactly equal to that which it would describe 
moving with accelerating velocity during the same time. Ac- 
cording to the preceding table, the velocity of a body at the end 
often seconds would be equal to twenty feet; now half that velo- 
city, or ten feet in a second, would carry a body through one hun- 
dred feet in ten seconds, which is precisely the space it would 
have fallen through in that time, by the effect of gravitation. 

83. Thus, the velocity acquired at the end of any given time 
being sufficient to have carried a body twice the distance it would 
reach with gradually accelerated velocity, it follows that the velo- 
city actually expended in the latter case is only half the velocity 
that has been acquired ; and since the final velocity in each se- 
cond is represented by a number double that denoting the time, 
the real amount of accelerating velocity may be expressed by 
a number equal to the time. Hence as the space fallen through 

With what velocity must a body move uniformly, in order to describe 
a given space in the same time as when uniformly accelerated by gravi- 
tation ? 

How may the real amount of accelerating velocity be expressed ? By 
what product may the space be represented ? 

E 



50 MECHANICS. 

by a gravitating body is equal to the square of the time, that is the 
number representing the time multiplied by itself, so the time and 
the velocity being equal, the space must be as the square of the 
velocity, or as the time multiplied by the velocity. 

84. We have already taken occasion to observe that the force 
of gravitation varies at different distances from the centre of attrac- 
tion; and hence the absolute effect o f gravitative influence must 
vary also. The consequence of this principle, as exemplified in 
the augmentation or reduction of the weight of bodies in different 
situations, has been pointed out. And since bodies in motion are 
acted on by gravitation in the same manner as bodies at rest, it 
follows that falling bodies will describe greater spaces in equal 
times, according to the increased intensity of gravitation, as occa- 
sioned by the diminution of the distance through which it acts. 

85. In order therefore to discover by experiment the force of 
gravitation, as measured by the space through which a body would 
fall, in a given time, as one second, we must know what is the 
distance of the gravitating body from the centre of attraction. If, 
as already remarked, the earth were a perfect sphere, every part 
of its surface would be equidistant from its centre; but, since it is 
an oblate spheroid, or globe flattened at the poles, the attraction 
must there be strongest, and must decrease in the intensity of its 
force, in the direction of a line from either of the poles to the 
equator. Such a line would be a meridian of longitude, and the 
degrees of latitude measured on it would be so many points at 
which the intensity of gravitation was progressively diminishing. 

86. Hence, in experiments made to ascertain directly the 
amount of gravitative force as measured by the space a body 
would fall through in one second of time, regard must be had to 
the latitude of the place where the experiment might be made, 
and if the utmost accuracy were required, the height of the spot 
above the level of the sea must also be taken into the account. 
These observations will be sufficient to show that no small degree 
of skill and attention w T ould be requisite in order to ensure the 
perfect exactness of such experiments. Instead therefore of pur- 
suing this train of investigation further at present, we shall pro- 
ceed to state that numerous and very accurate experiments have 
been made, whence it appears that in the latitude of London, 
which is near the level of the sea, a heavy body falls, from the 
action of gravity, in the first second of its descent, through the 
space of sixteen feet and one inch, or 193 inches. 

87. In making calculations relative to the phenomena of falling 
bodies, when extreme accuracy is not required, the space passed 

What will enable us to discover by experiment the force of gravita- 
tion ? 

How does the figure of the earth affect its force of attraction at the 
different parts of its surface ? Through what space will a body fall in 
the first second in the latitude of London ? 

What may generally be assumed for the space described in one second 
by a body falling freely ? 



RATE OF VELOCITY OF FALLING BODIES. 



51 



through in one second of time may be estimated at 16 feet; and 
taking- this as the common multiple of distances and velocities, a 
table similar to that already given may be constructed, by means 
of which the spaces fallen through in any given time may be 
ascertained with sufficient exactness. The following short speci- 
men of such a table may be easily extended by the young stu- 
dent, so as to afford data for the resolution of several interesting 
questions. 



Seconds of 
descent. 

1 . 

2 . 

3 . 

4 . 

5 . 



Feet passed 

through at the end 

of each second. 

16 

64 

144 

256 

400 



Final velocity 
in each second. 

32 

64 
96 

. 128 
. 160 



Feet passed 

through in each 

second. 

16 

48 

80 

. 112 

. 144 



88. Suppose now we wish to discover the height of an emi- 
nence, or the depth of a well ; by dropping a leaden bullet from the 
top of either, and observing how many seconds elapsed before it 
reached the bottom, a table like the above would show by inspec- 
tion how many feet the space amounted to in eithei case. No 
notice, however, is here taken of the resistance of the air, which 
would greatly affect the motion of bodies falling from a consider- 
able height. Several years ago a man dropped from the balcony 
of the Monument, near London Bridge, a height of about 200 feet : 
he would therefore have fallen to the pavement below in nearly 
three seconds and a half, but for the resistance of the atmosphere ; 
notwithstanding which he must have been whirled downwards 
with a velocity, which perhaps rendered the miserable being in- 
sensible of the appalling catastrophe that awaited him. Some- 
times aerolites have exploded in the air, and fallen in showers of 
meteoric stones, as happened near Sienna, in Italy, in 1794; and 
at L'Aigle, in France, in 1803. If the moment of such an explo- 
sion could be observed, and also that at which the stones, or any 
one of them, came to the ground, the height at which the pheno- 
menon took place might be estimated with tolerable accuracy. 

89. The obstacles which occur in the experimental investigation 
of the laws of gravitation are partly owing to the very extensive 
space that would be required for direct experiments on falling 
bodies, even for a few seconds ; and to these would be added the 
variable effect of atmospheric pressure against bodies moving with 
great velocity. The consideration of these difficulties led Mr. 
George Attwood, an ingenious philosopher who died in the early 
part of the present century, to contrive a machine in which the 
influence of gravitative force might be moderated without destroy- 
ing its characteristic efficiency, in the production of an accelerated 

How might the height of an explodin-g meteor he estimated ? 
What obstacles occur in the direct experimental investigation of the 
laws of falling bodies ? 



52 



MECHANICS. 



A 




motion. This piece of machinery was very elabo- 
rately constructed, and some parts of it could not be 
correctly described without entering - into extensive 
details, and giving - delineations on a large scale, 
but the principle on which it acted may be concise- 
ly explained. Equal weights A and B, being - sus- 
pended by a fine silken cord, passing over a whee: 
moving with the least possible degree of friction ; 
then by adding a certain quantity to one of the 
weights, as by placing on it a small bar C, de- 
, scending motion may be produced, differing in in- 
tensity from that caused by the unrestrained power 
of gravitation, but obeying the same law of accelerating velocity ; 
so that, though the loaded weight might be made to descend only 
one inch in one second, its continued motion would be found to 
proceed in the regular ratio of the squares of the times of descent. 

90. It might be imagined, that as the large weights counterba- 
lance each other, the small bar ought to descend as freely as if 
they were removed ; but the gravitating force expended in pro- 
ducing motion is partly consumed in overcoming the inertia of tne 
large weigh s, and therefore the portion of it which acts as amov- 
ing power v. ill bear the same proportion to the whole force, as 
the weight of the bar alone bears to the entire moving mass, /or 
it is expended in drawing down the loaded weight A on one side, 
and raising the weight B on the other side, at the same t±rne. 
Thus if the weights were two pounds each, and the bar weighed 
but half a pound, the force expended would, be but one-ninth part 
of the whole force; and the loaded weight A would descend but 
one-ninth part of sixteen feet in the first second, of time, and with 
the same reduced velocity, as the squares of the times, throughout 
its descent. By means of this machine a variety of most interesting 
and important experiments may be performed, and the laws of 
gravitation satisfactorily demonstrated. 

91. Bodies projected directly upwards will be influenced by 
gravitation in their ascent as well as in their descent ; but its force 
must be calculated inversely, producing continually retarded mo- 
tion while they are rising, and continually increasing motion dur- 
ing their fall. So that a body propelled perpendicularly through 
the air, leaving out of the question the resistance of the medium 
through which it passed, would, rise to a height exactly equal to 
that from which it must have fallen to acquire a final velocity the 
same as it had at the first instant of its ascent. And the velocity 
would be the same in the corresponding parts of the ascent and 
descent. The time likewise which the propelled body required 
to attain its utmost height would be just equal to that during 



Describe the principle of Attwood's machine. What portion of the 
gravitating force of the bar added to one of his equal weights is employed 
in producing motion ? 

What laws of motion apply to bodies projected directly upwards ? 

What relation exists between the times of their ascent and descent ? 



MOTION OF BODIES ON INCLINED PLANES. 



53 



which it would be falling to the ground. Hence the laws which 
regulate uniformly accelerated velocities will apply equally to uni- 
formly retarded velocities : that is, the velocity lost in any given 
time, by the influence of a uniformly retarding force, will be as 
the time ; the space passed through as the square of the time, or 
the square of the velocity ; and so on, as in the case of accelerat- 
ing forces. 



Motion of Bodies on inclined Planes and Curves. 

i 92. Among the varieties of accelerated motion depending on 
the influence of gravitation, that of bodies passing along inclined 
planes requires to be noticed, as exhibiting the modified effect of 
a most extensively acting force. When pressure is applied in a 
vertical direction to a body supported by a horizontal plane, it is 
manifest that no motion can ensue ; and the force of gravitation 
thus acting can be measured only by the direct weight of the 
body so situated. But if the plane surface on which the body 
rests be inclined in any degree, the efficient weight will be pro- 
portionally diminished; and if the inclination of the plane be suf- 
ficient to enable the body to overcome the resistance to its motion 
arising from friction and similar causes, the body will move dowi 
the plane with a velocity so much the greater as the surface ovei 
which it moves approaches to a vertical direction. The motion 
in this case will be a continually accelerated motion, differing in 
degree of relative velocity from that caused by the direct influence 
of gravitation, but subject to the same law of acceleration. 

93. In order to estimate the force with which bodies are im- 
pelled down inclined planes, we omit for the present all conside- 
ration of the resistance occasioned by friction ; and therefore sup- 
pose a plane to have a perfectly smooth surface, and the figure of 
the moving body to be globular, and of the same density in every 
part, so as to be capable of motion in any direction. 

94. Let A C represent the declivity of 
an inclined plane, A B its perpendicular 
height, and D E the absolute weight of 
an ivory ball on its surface ; now this 
weight, by the parallelogram of forces, 
will be found to act in two directions ; 
D F, or G E, denoting the direct pres- 
sure perpendicular to the declivity of the 
plane, and D G, or F E, in the direction 
of that declivity : the former force it is 

Ho\v can the force of gravitation in a body pressing a horizontal plane 
be measured ? What effect on the pressure of the plane will result from 
its becoming inclined ? When will motion commence on the inclined 
plane ? 

Of what nature will be the motion over the inclined plane ? 

What circumstances are we to omit in first estimating the force of 
motion on inclined planes ? Describe the diagram relating to this sub- 
ject. 

E 2 




MECHANICS. 




obvious will be destroyed by the resistance of the plane, and the 
ball will consequently move down the plane with a force bearing 
the same relation to the force of gravity that D G does to D E, 
that is, it would move down the plane through a space equal to 
D G, while it would fall through a space equal to D E by the 
force of gravitation. 

95. Whatever may be the declivity or inclina- 
tion of the plane, the force of a body moving down 
it may be estimated on the same principle. Thus 
suppose the obliquity of the plane to be very con- 
siderable, as represented in the margin, the line 
D G would be nearly equal to D E ; and the force 
of the body moving on such a plane would mani- 
festly be little inferior to that of the same body 
falling - free!)'. 

As the force of a body moving on an inclined 
plane is less than that of a body moving by the 
influence of gravitation, its final velocity in a given time must also 
be less ; and the distance through which it must move on a decli- 
vity to acquire a certain final velocity must be greater than that 
through which it must fall freely by the effect of gravity to ac- 
quire the same velocity. 

j^ 96. It may be demonstrated that a 

body moving down any inclined plane 
will acquire the same final velocity, in 
passing from A to C, that it would have 
gained in falling through the relative 
distance A B. For let A D be the 
space through which the body would 
move down the plane in the same time that it would fall from A 
to B, it follows that, in order to acquire the same velocity that it 
would gain by falling from A to B, it must pass through a space 
bearing the same proportion to A B that A B does to A D ; and 
as the triangles A D B and A B C are similar, their correspond- 
ing sides must have the same relations to each other; therefore 
A D will be to A B, as A B to A C. Hence the proposition will 
universally hold good, that a body rolling down an inclined plane 
of any extent or obliquity, but for the effect of friction or similai 
causes, would acquire the same final velocity, as if it had fallen 
directly through a space equal to the perpendicular height of the 
summit of the plane. 

97. Bodies moving on curved surfaces would not exhibit uni- 
formly accelerated velocity, like those moving on inclined planes ; 




What relation will the final velocity of a body moving on an inclined 
plane, bear to that which it would acquire in falling perpendicularly 
through the same distance? 

What relation will the velocity of a body falling freely, and of one de- 
scending an inclined plane, bear to the length and height of the plane ? 

With what sort of velocities will a body move down a curved surface? 

Why would not the motion be uniformly accelerated ? 



MOTION OF BODIES ON CURVED SURFACES. 



55 



for the resistance occasioned by the peculiar form of the carve in 
which any such body might move would be continually changing 1 , 
and the result of that resistance would be a consequent change in 
both the velocity and the direction of the moving body. Some 
idea of the nature of this perpetual change may be obtained from 
considering what would be the effect of presenting to a moving 




body a succession of inclined planes, either ascending or descend- 
ing, the outline of which would form a rude resemblance to a 
curved surface. From the mere inspection of the preceding 
figures, it may be comprehended that a body passing over a con- 
vex surface, as from A to B, would encounter a perpetually dimi- 
nishing resistance ; and in passing over a concave surface, as from 
C to D, the resistance would progressively increase. For in the 
former instance, the effect would be as if the moving body rolled 
down a number of declivities, each one more oblique than the 
preceding ; and in the latter, it would be as if the body passed 
over a series of declivities, each of which approached nearer than 
the preceding to the figure of a horizontal plane. 

98. Having thus endeavoured to explain the manner in which 
curvilinear motions are produced by the constant action of variable 
forces, we can now proceed to investigate the phenomena of cur- 
vilinear motions in general. When a body moves through an 
entire circle, with uniform velocity, as it must be impelled by 
forces continually varying in intensity and direction, those varia- 
tions must be supposed to take place momentarily, or in incon- 
ceivably minute portions of time and space. So that such a body 
might be considered as moving in the circumference of a polygon 
having an infinite number of sides. 

99. In the case of a body moving over a curved surface and in 
contact with it, there must be a certain pressure of the body on 
the surface over which it passes, and a corresponding resistance, 
or pressure on the body, in every instant of its progress. Now 
this pressure shows the degree of force to which the continual va- 
riation of direction, or deflection of the moving body is to be attri- 
buted. Suppose a leaden bullet, or a billiard-ball to be made to 
move round within a hoop laid flat on a table or any level surface, 
it would obviously press against the inside of the hoop, thus ma- 



How are the forces Avhich impel a revolving body supposed to vary ? 

Into what figure may we conceive the circle to be resolved ? 

How would a body moving within a curved surface be affected by it;' 



56 MECHANICS. 

nifesting a constant tendency to escape from the circle in which 
it was moving, and only withheld by the counterpressure, or re- 
sistance of the hoop. If then the hoop were suddenly lifted while 
the ball was passed round within it, the circular motion would no 
longer be continued; but the ball would fly off in a right line 
from the point where it was set at liberty. The force operating 
on the moving body in this case would be precisely similar to that 
which would propel forwards a stone discharged from a sling, on 
letting go the cord which retained it during the previous circular 
motion or whirling, whence it would acquire its subsequent ve- 
locity. 

100. The forces which act on bodies revolving in circles or 
other orbits may be regarded as antagonist powers, one of which 
perpetually impels the moving body in a right line from the cen- 
tre of motion, and the other draws it towards that centre ; and by 
the joint action of these forces curvilinear motion is produced. 
The former, or the repellant power, is named centrifugal force, or 
force causing bodies to fly from a centre ; and the latter is styled 
centripetal force, or that which attracts moving bodies towards the 
centre of motion. 

101. These opposing forces have also received the common ap- 
pellation of central forces. It may be here observed that the line 
in which a body will move, on escaping from the circle around 
which it must have been previously whirled, will always form a 
tangent to that circle, or in other words, it will extend in a direc- 
tion perpendicular to another line drawn from the centre of the 
circle to the point of escape. Hence this force has been sometimes 
called a tangential force ; but its usual appellation is that of cen- 
trifugal force. 

102. These forces must necessarily differ in degree according 
to circumstances, — such as the mass of the moving body, the ex- 
tent of the circle in which it may move, and the velocity of its 
motion. 

Thus a ball, B, of two pounds weight, 
would require a greater centrifugal force to 
make it revolve round the circle A, in any 
given time, than another ball weighing only 
one pound. The extent of a circle is to be 
estimated by its radius, or the line C B, 
passing from its centre to some point in its 
circumference, and consequently always 
equal to half the diameter. Now the centrifugal force or pres- 

What line would such a body describe, if suddenly relieved from the 
confinement of the curved surface ? 

How may we explain the motion of a stone discharged from a sling? 

What is meant by the terms centrifugal and centripetal, as applied to 
forces ? What common appellation 'is applied to them ? When a body 
escapes from the influence of its centripetal force, what will he the line 
of its subsequent path ? What is signified by the term tangential force? 

By what circumstances are central forces caused to vary their inten- 
sity ? Exemplify the principles applicable to this variation. 




CENTRIFUGAL MOTION. 57 

sure must increase, as the radius of the curve in which a body- 
moves increases. In a circle the same radius will apply to every 
part ; but if a body should move in any other curve, as an el- 
lipse, the degree of curvature, and consequently the length of 
the radius, will differ in different parts. Hence the expression, 
radius of curvature, has been used to denote the line which may 
be drawn from the centre of motion to any given point of the 
curve described by a revolving body. The velocity of revolving 
bodies may be estimated by the actual space passed through in a 
given time, or by reference to the time in which any such body 
would pass from one point in the circuit in which it moved to an- 
other point. These distances, being measured by the angle form- 
ed by lines drawn from the centre of motion to the points just 
mentioned, the velocity indicated may be styled the angular ve- 
locity of the moving body. 

103. The amount of centrifugal force in different circumstances 
may be experimentally determined by means of a machine called 
a whirling table, which is so constructed that different weightsV 
may be whirled at any given distance from the centre of motion,* 
and with any required degrees of velocity ; and the measure of 
the centrifugal force expended is obtained by causing the revolving 
weights, by their rotatory motion, to draw up other weights, which 
are suspended freely; and thus the effect of centrifugal force maybe 
ascertained in a satisfactory manner. From the results of experi 
ments with the whirling table, it appears, that the centrifugal 
force will increase as the mass of the moving body increases ; 
that the centrifugal force will be doubled, other circumstances re- 
maining the same, if the radius or curvature be doubled ; that if 
the radius of curvature remain the same, arid the angular velocity 
be doubled, the centrifugal force will be quadrupled ; and that if 
equal masses be made to revolve within circles, the radii of 
which are as 2 to 3, and with angular velocities as 1 to 2, the 
centrifugal force will be as 2 to 12, or as 1 to 6. Hence it ap- 
pears that the centrifugal force increases in direct proportion to 
the mass of the moving body, and to the distance from the cen- 
tre of motion, and also as the square of the angular velocity. 
Thus : — the radius of the circle being 2 — the angular velocity l, x 
the square of which is 1— the centrifugal force will be the pro^ 
duct, 2x 1=2 ; the radius of the circle being 3 — the angular ve- 
locity 2, the square of which is 4 — the centrifugal force will be 
the product, 3x4=12 ; thus, as above, the centrifugal force in 
the different cases would be as 2 to 12. 



What is meant by radius of curvature * 

In how many ways may the velocity of a revolving body he estimated? 

What is meant by angular velocity? 

What apparatus is employed to demonstrate the laws of centrifugal 
forces ? 

What relation have these forces to the masses of the revolving bodies? 
What relation to the radius of curvature ? What to the angular velo- 
city ? 



58 MECHANICS. 

104. In order to obtain the amount of centrifugal force at any 
given point, the square of the number of feet expressing the an- 
gular velocity in one second of time must be divided by the num- 
ber of feet denoting the radius of curvature, and the quotient will 
give the centrifugal force, as estimated by the number of feet a 
body impelled by it would describe in one second. Thus, a sling, 
two feet long, circling vertically, with the velocity of eight feet 
each second, would communicate to a stone a centrifugal force 
equal to thirty-two feet in a second, which would be the final ve- 
locity of a body falling during one second, and the centrifugal 
force therefore would be just sufficient to counteract the influence 
of gravitation, and enable the sling to support its load. If the 
motion of the sling were accelerated so as to perform a complete 
revolution in one second, the tension of the string would uphold 
the stone with a force 2^ times greater than the attraction of gra- 
vitation. 

105. An amusing experiment, illustrative of the influence of 
centrifugal force in overcoming that of gravitation, may be per- 
formed by placing a tumbler filled with water, in a sling, or fix- 
ing it upright in the bottom of a net, when it may be whirled 
round with such velocity that not a drop of the water will be 
spilled, though the mouth of the glass will be turned downwards 
during a part of each revolution. 

106. The centrifugal force at the equator may be computed by 
taking the time of one diurnal revolution=86,164 seconds, the 
equatorial radius of the earth=20,9'21,185 feet, and the ratio of 
the earth's circumference to its diameter=3.14159:l. Then 
4x3.141592x20,921,185-h86,164 2 =0.1,112,259, which is the 
centrifugal force at the equator. Now as the actual force of gra- 
vitation, determined by experiments, the nature of which will be 
subsequently described, is, 32.08818 ; and therefore, it the earth 
were at rest, it would be 32.08818+0.1,112,259=32.1,994,059, 
it follows that the centrifugal force at the equator is to the force 
of gravity in the proportion of the numbers 0.1,112,259 to 
32.1,994,059, or nearly as 1 to 289. So that the force of gravita- 
tion is 289 times greater than the centrifugal force, at those parts 
of the earth's surface where the action of the latter is most pow- 
erful. 

107. Now since 289 is the square of 17, it will follow that if 
the diurnal revolution of the earth had been completed in one- 
seventeenth part of the time, which it now takes up ; that is, had 

How may we obtain the amount of centrifugal force at any given point ? 

How may we compare centrifugal force with that of gravitation ? 

How may it be familiarly shown, that this force is often superior to 
that of gravitation ? 

How may we compute the centrifugal force of the earth at the equator ? 

What is the actual force of gravitation there, as determined by experi- 
ment ? What is the amount of centrifugal force, and by how many times 
does the former exceed the latter ? 

How much must the velocity of (he earth's revolution be increased, in 
arder that bodies at the equator should lose all their weight? 



VIBRATION OF PENDULUMS. 59 

the earth revolved on her axis m eighty-four minutes, instead of 
nearly twenty-four hours, the centrifugal force would have coun- 
teracted that of gravitation, and all bodies would have been abso- 
lutely destitute of weight ; and if the centrifugal force were further 
augmented, the earth revolving in less time than eighty-four 
minutes, gravitation would be completely overpowered, and all 
fluids and loose substances near the equinoctial line would fly off 
from the surface. 

108. Among the abundant examples of the effects of centrifu- 
gal forces that might easily be adduced, a few may here be no- 
ticed, in addition to those already given. The astonishing power 
of this force, even when exerted on a small scale, appears from 
its destructive influence on hard solid bodies ; as when grindstones 
are whirled about with extraordinary velocity in our manufacto- 
ries, they will sometimes split, and pieces fly off with amazing 
force. The more regulated, but no less powerful operation of 
centrifugal force may be observed in some parts of the machinery 
employed in certain branches of the arts : as in the fly-wheel 
which regulates the motion of a steam-engine, and in the coining 
press; but these and other modifications of mechanical power will 
be noticed elsewhere. Semifluid and soft but tenacious sub- 
stances, under the influence of centrifugal force, assume in a 
greater or less degree the form of a compressed globe ; and thus 
a rudely-shaped ball of clay, placed on a potter's wheel, with the 
assistance of gentle pressure while in the state of revolution, gradu- 
ally acquires a symmetrical form ; and globular glass vessels owe 
their figure to the analogous manipulations of the glass-blower. 
Liquids exposed to a whirling motion are similarly affected ; as 
may be perceived if a glass of water be suspended by threads, 
and made to turn with great velocity by the twisting and untwist- 
ing of the threads, when the water would sink in the centre, and 
rise on the sides so as to escape in part over the edge of the glass. 
In all cases centrifugal force tends to make bodies under its influ- 
ence recede from a central point, and when it acts in conjunction 
with a centripetal force, the effect will be revolving motion, 
whether those powers be exerted in keeping a peg-top, or a tee- 
totum spinning on a floor or table, for a few minutes ; or in caus- 
ing the vast globe which we inhabit to revolve with undiminished 
energy through countless ages. 

Oscillation of the Pendulum. 

109. Oscillation or vibration is a peculiar kind of curvilinear 
motion, depending on the influence of gravitative attraction, and 
it not only affords the means for ascertaining the variation of the 
force of gravitation in different latitudes, but likewise furnishes 

Give some examples of the effects observed to result from centrifugal 
force. 

What is meant by oscillation ? 

To what purposes in science and arts is it applicable? 



60 MECHANICS. 

the most accurate method for measuring time, and leads to vari- 
ous important results in the investigation of many natural pheno- 
mena. 

110. When any heavy body is suspended by a string or small 
wire, it will take a direction in a line vertical to that point of the 
earth's surface over which it hangs, as in the case of the plumb-line 
of a mason's level when placed on a horizontal plane. Now the 
laws of oscillation are those which would regulate the motion of a 
body thus suspended, if drawn aside from the vertical line in which 
it would rest, and then let go and suffered to oscillate or swing for- 
wards and backwards undisturbed. In treating this subject it will 
be most convenient to consider the phenomena of oscillatory mo- 
tion simply and independently of the effects of the resistance of 
the air, the friction of the suspending line on the point of suspen- 
sion, and the varying extension of that line ; all which it is obvious 
would affect the results of actual experiments, and would therefore 
require attention in making calculations founded on them. 

111. Suppose A B to represent a pendu- 
lum at rest in the vertical position, if it be 
then drawn from B to C and let fall, it will 
\ return to B, with an accelerated motion, 

which, however, will not be uniformly ac- 
celerated, since it must depend partly on 
the gravitation of the pendulum towards 
the earth, which acting alone would cause 
b it to fall perpendicularly from the point C, 
c but which being modified by the tension of 
B the line, it is forced to describe the arc C 

B. Now at B the direct power of gravitation will be not merely 
modified but destroyed, for the line being stretched to its full 
extent would prevent any further descending motion; but when 
arrived at B, the pendulum would have acquired a certain degree 
of velocity during its previous descent, which would be just suffi- 
cient to overcome the force of gravity tending to retain it at the 
point B, and make it move forward from that point to D, with a 
retarding velocity, which would there be entirely expended; and 
since the pendulum at D would be in a situation exactly correspond- 
ing with that in which it was placed at C, it must again describe 
the same arc D B C, but in a retrograde direction, first with a 
gradually accelerated velocity, and then with a velocity progres- 
sively retarded. Thus, but for the obstacles already mentioned, 
and the wear and tear of materials, a pendulum, once put in a 
state of vibration, would go on regularly oscillating for ever. 

112. The vibrations of any one pendulum will be described in 
equal times whatever be the extent of the arc through which it 
moves, provided that arc do not exceed a certain limit. 



What circumstances affect the results of experiments on oscillation ? 
What forces combine to produce oscillatory motion ? What causes 
the ascending part of an oscillation ? 



NATURE OF OSCILLATORY MOTION. 61 

Thus when the vibration of a pendulum 
is progressively weakened by the resist- 
ance of the air, every succeeding- arc 
passed through will be less than the fore- 
going; and yet it will be found that though 
the pendulum moves slower and slower 
continually, there will be but little dif- 
b ference in the time taken up by the ball 
X%\J>£ i 11 moving from 5 to 5, 4 to 4, &c, on 
each side of the line A B, till it stops 
(S entirely. It is this remarkable property 

s of the pendulum that makes it so useful 

as a measure of time ; and clocks, or time-keepers, regulated by a 
pendulum, are nothing more than trains of wheel-work kept in 
motion by weights, and so arranged as to register the beats of 
pendulums which oscillate seconds. This equality of vibration 
of bodies in certain curves was discovered by Galileo, whose 
attention is said to have been excited by remarking the motion of 
a chandelier hanging from the ceiling of a church at Pisa ; for, 
noticing that it moved with uniformity as to time, independent of 
the space passed through, he was induced to make experiments, 
which established what has been termed the law of Isochronism, 
or equality of time.* 

1 13. As it is only when oscillating in very small arcs of circles that 
pendulums preserve this regularity of vibration, it became a sub- 
ject of inquiry among philosophers whether a curve could not be 
found in which the isochronism of a pendulum would be perfect ; 
and such a curve was discovered by the celebrated Dutch mathe- 
matician, Huygens, the contemporary of Newton. It has been 
named a cycloid, f and from its property an isochronal curve, and 
it differs little from an arc of a circle, except in rising somewhat 
more abruptly at each extremity. But it is the less necessary to 
enter into any further description of its nature and properties, as 
it has been found after all to be less adapted for practical purposes 
than small circular arcs, in which therefore the pendulums of time- 
keepers are made to oscillate. 

114. The vibrating weight of a pendulum does net influence its 
motion ; for whether a great or a small weight be affixed to a 
vibrating line, its oscillations will be similar, provided the length 
of the line, measured from the point of suspension to the centre 
of oscillation, remains the same. Sir Isaac Newton made experi- 

What is meant by the isochronism of oscillations ? By Avhom was this 
character discovered ? 

In what form of curve must oscillations be performed, in order to be 
isochronous ? 

What influence has the weight of a pendulum on the time of its oscil- 
lation ? 

* From the Greek i s o s , equal, and Xpsvos, time. 

f From the Greek Kux^os, a circle, and e.Jo,-, a resemblance. 

F 



62 MECHANICS. 

ments on a great variety of substances, as metals, stones, woods, 
salts, portions of flesh, &c., whence he ascertained that how 
greatly soever they might differ in weight, the addition of any of 
them to a pendulum would not interfere with its rate of oscillation, 
so long as its length remained unaltered. Thus, as heavy bodies 
and light ones would fall to the earth, through a given space, in 
the same time, but for the resistance of the air, so they would be 
found to vibrate in equal times at the end of a line of a given 
length, provided atmospherical resistance could be made to act on 
them in the same manner, or be entirely excluded, as by inclosing 
the vibrating bodies in an exhausted receiver. 

115. It is on the length of the pendulum that the rate of oscilla- 
tion principally depends ; that is, the greater the distance between 
the point of suspension and the point of oscillation, the longer will 
be the period of each vibration ; and on the contrary, the shorter 
that distance, the quicker will the vibrations take place. Now, 
as gravitation is the power on which oscillatory motion depends, 
so the same law that regulates its operation on falling bodies is 
observable in its action on oscillating bodies : for as the intensity 
of gravitative force decreases as the squares of the increasing dis- 
tances of bodies, thus the time of a vibration will increase as the 
square root of the length of the pendulum, or the distance from 
the point of suspension to the point of oscillation, increases. If 
then a pendulum 1 yard in length, would make one vibration in 
one second, a pendulum i of a yard long would vibrate half 
seconds, one 4 yards long, would vibrate once in two seconds, 
one 9 jrards long, in three seconds, and so on ; for ^ is the square 
root of a, 2 of 4, 3 of 9, &c. 

116. But in order to obtain the absolute length of a pendulum 
that would swing seconds, it is necessary to take into considera- 
tion the intensity of gravitation, which, as already stated, varies 
at different parts of the earth's surface, depending on their rela- 
tive distance from the centre of gravitative attraction. The 
greater the intensity of gravitation at any place, so much' the 
quicker will be the vibrations of a pendulum of a given length : 
so that a pendulum which would oscillate seconds at London would 
perform each of its oscillations in somewhat less than a second, if 
it could be removed to the north pole ; and on the contrary, would 
take up more than a second in one vibration under the equinoctial 
line. 

117. The intensity of gravitation at any given point of the 
earth's surface thus corresponding with the vibrations of a pendu- 
lum of a given length, it follows that if the intensity of gravita- 

What resemblance in this respect has the pendulum to bodies falling 
freely ? 

On what circumstance in a pendulum does the time of its oscillations 
depend ? Between what two points is the true length of a pendulum to 
be taken ? Illustrate the law ot* its motion by an example. 

What local circumstance must be tffken into view in obtaining the ab- 
solute length of a pendulum ? 



RELATIVE LENGTHS OF PENDULUMS. 63 

ticn at any place, as estimated by the space which a body falling 
freely would describe in any time, as one second, be known, the 
length of a pendulum, which would vibrate seconds at that place, 
may be ascertained by computation. For since the time of vibra- 
tion is to the time of descent through half the length of the pendu- 
lum, as the circumference of a circle to its diameter, that is, as 
3.14159 to 1, let the time of vibration be 1 second, then the length 
of the pendulum may be thus found : the time of descent of a 
body during 1 second, in the latitude of London, by the influence 
ofgravitation, has been already stated to be about 16 1-12 feet, orl93 
inches ; and since the spaces of descent are as the squares of the 
times, therefore 37141592 ; p : : 193 : 19.0625=19 l-16=half the > 
length of the pendulum, which must therefore be 19 1-16 x 2=39£ ' 
inches. 

118. In order to determine the length of a second's pendulum 
by experiment, a pendulum of a known length must be made to 
oscillate for a certain time, as one hour; then the square root of 
its length will be to the square root of the length of the required 
pendulum, inversely, as the number of vibrations performed in 
an hour, by the pendulum which has been the subject of the 
experiment, to the number of seconds in one hour. Thus, if in 
any latitude it could be ascertained that a pendulum 9 yards in 
length oscillated 1200 times in an hour, then as the number of 
oscillations, 1200, to the square root of the pendulum, 3, the 
square root of 9, so inversely would 3600, the number of oscilla- 
tions required to be performed by the seconds pendulum, be to 
the square root of its length: that is, as 3600 : 3 : : 1200 : 1 ; 
since 1200x3-4-3600 = 1, the square of which would be 1; 
therefore a pendulum 1 yard long would swing seconds in any 
place where a pendulum 9 yards in length would make but 1200 
vibrations in an hour. 

119. It will be obvious, from what has been already stated, 
relative to the effect of friction, atmospheric resistance, and the 
extensibility of the line of suspension of a pendulum, that a mul- 
titude of precautions would be requisite in making direct experi- 
ments on the lengths of pendulums, with reference to the times of 
vibration at any given place. Dr. Halley, in the early part of 
the last century, estimated the length of a second's pendulum at 
39.125 inches, = 39f inches; and that estimate has been general- 
ly adopted, as sufficiently correct for practical purposes. From 
the most recent and accurate researches of men of science, it 
appears that the length of a pendulum which oscillates seconds, 
in vacuo, at the mean temperature of 62 degrees of Fahrenheit's 
thermometer, in the latitude of London, 51° 31' 8" N., must be 
39.13929 inches : and as the further result of experimental inves- 

By what proportion may we find the length of a second's pendulum, 
when we know the intensity of gravitation ? 

Mow may that length he ascertained by experiment ? 

State some of the lengths actually found necessary in different parts 
of the earth, in order to produce the same number of beats per hour. 



64 MECHANICS. 

ligation, it may be added that at Melville Island, in the Polar Sea, 
Lat. 74° 47' 12" N., the length must be 39.207 inches ; at the 
Galapagos Islands, Lat. 32 / N., 39.01719 inches ; and at Rio 
Janeiro, Lat. 22° 55' S., 39.01206 inches.* 

120. As the force or intensity of gravitation decreases as the 
distance from the earth's centre increases, it follows that a pendu- 
lum, which would oscillate seconds at the bottom of a mountain 
one mile in perpendicular height, would not perform so many 
complete oscillations as there are seconds in an hour, if removed 
to the top of the mountain. Suppose the radius of the earth's 
circumference to be 4000 miles, as a second's pendulum would at 
that distance from the centre of attraction vibrate 3600 times in 
an hour, and therefore 86400 = 3600 X 24 in a day, it follows that 
it would lose the 4000th part of 86400 seconds in a day, at the 
distance of 4001 miles from the earth's centre. Now 86400-r- 
4000 = 21.6, that is, the loss would be 21.6 seconds in a day. 

121. The length of a pendulum vibrating seconds being known, 
that of one which will vibrate half seconds, like those in most 
table clocks, or any other portion of time, may be readily calcu- 
lated. For the times of vibration being as the square roots of the 
length of the pendulum, hence, as one second to 6.255, the square 
root of 39.125, so will half a second be to the square root of the 
pendulum required ; that is as 1 : 6.255 : : 0.5 : 3.1275, the square 
of which will be 9.78. But the length of the half seconds, or any 
other pendulum, may be also found by taking the squares of the 
times, which will be directly as the lengths of the pendulums ; 
thus as(l = l 2 )sec. : 39.125 : :(.25 = ^jsec. : 9.78, as before, or 
9.7 inches, the length of a half second's pendulum. 

122. A pendulum may be so constructed as to have its centre 
of oscillation far beyond the limits of its actual dimensions ; and 

thus a pendulum only one foot in length, may be 
made to oscillate as slowly as another 12 feet 
long. Suppose a rod of iron, A B, to be loaded 
at both ends, and suspended at C, so that it 
might vibrate freely, it is manifest that though 
the arc described in each vibration would be 
limited by the length measured from the point 
of suspension, the velocity of the ball B, would 
, be checked by the counterweight of the ball A, 
^""^ly^"" an( l tne latter being moveable on the rod, the 
rate of vibration might be regulated at pleasure. 

What would be the effect on the rate of a clock, of canning it to the 
top of a high mountain ? Why ? 

How may we calculate the true length of pendulums to vibrate ip 
other times than seconds, when that of the latter is known ? 

How may the centre of oscillation be carried beyond the limits of a 
pendulum ? Will this increase or diminish the number of its oscilla- 
tions in a given time ? 

* See Abstracts of Papers printed in the Philosophical Transactions, 
from 1S00 to 1830, vol. ii. p. 144, and p. 194. 



CENTRE OF GRAVITY. 65 

An instrument of this kind, called a Metronome, is used to mark, 
by its oscillations, the time in performing pieces of music. 

123. A rod of uniform dimensions might be made to vibrate as 
a pendulum, without any ball or appendage whatever ; but in that 
case the centre of oscillation would be raised, and such a pendu- 
lum must consequently be longer than one of the usual form. In 
a uniformly shaped rod or bar suspended at one extremity so that 
it might vibrate freely, the centre of oscillation would be at two- 
thirds of the distance between the point of suspension and the 
other extremity of the rod. Force applied at that part to arrest 
the motion of the rod would take complete effect, but at any other 
part a stroke would cause a tremour or irregular action of the 
moving body. Hence this point has been called the centre of 
percussion. In using a weapon of considerable length and nearly 
the same size throughout, as a cudgel or a sabre, the most effective 
stroke would be when the point of impact coincided with the cen- 
tre of percussion; the situation of which must be at about two- 
thirds of the length of the weapon, its exact place depending 
chiefly on the relative weight of that extremity with which the 
blow is inflicted. 

Centre of Gravity. 

124. In every body or mass of matter at rest, there must be a 
certain point, in the direction of which, any force acting parallel 
to the surface on which the body is placed, will either be resisted 
by the weight and friction of the mass, so as to produce no effect, 
or if it be sufficiently powerful to overcome the resistance, the 
body will move in the direction of the force applied ; but the same 
force acting against any part of the surface of the mass, not hori- 
zontally nor perpendicularly opposite to the point already men- 
tioned, may cause the body to vibrate or be overturned, according 
to circumstances. This point is commonly called the centre of 
gravity, and sometimes the centre of inertia ; and from the pro- 
perty just stated it might be termed the point of greatest resist- 
ance. 

125. The annexed figure will serve to exemplify the phenome- 
non now described. Let A be the centre of gravity of a solid 

body with a hemispherical base resting on a 
horizontal plane, then if pressure be applied 
vertically at E, it is manifest that it can pro- 
duce no motion ; but if applied at B, directly 
opposite to the centre of gravity, its effect will 
depend on the degree of force, as a small force 
will be destroyed by the inertia of the solid 

What substitute might be employed as a pendulum instead of the rod 
and balls ? 

Where would the point of oscillation of such a pendulum be found ? 

When such a pendulum is to be suddenly arrested, where must the re- 
sistance be applied ? Describe and illustrate the centre of percussion } 

What is meant by the terms " centre of gravity," centre of inertia," 
and " point of greatest resistance," when applied to bodies ? What slates 




66 MECHANICS. 

mass, while a great force will be partly employed in counteracting 
the inertia, and partly in propelling the mass steadily along the 
level plane. Now if force be applied at C or D, or any other 
point above or below B, it will have some effect, however incon- 
siderable, causing the body to rock or vibrate, if the force be 
small, and to be overturned if the force be great. 

126. The centre of gravity in all bodies is that point at which 
the influence of gravitation seems to be concentrated ; and hence, 
in any body, unless that point be supported, motion will take 
place, and be continued till the body settles in a position in which 
the centre of gravity cannot sink lower. Therefore when no ob- 
stacle is opposed to the motion of a body, either by its peculiar 
figure or that of the surface beneath, it will always take such a 
position that a line drawn from the centre of gravity to the point 
where the body comes in contact with the surface below it will 
be the shortest that can be drawn from the centre to any part of 
its superfices. Thus an oviform body, placed as in the annexed 
figure, would not stand in the position represented, but would turn 
till the shorter line, A C, became perpendicular to the supporting 
surface, instead of the longer line A B. 

127. If a body be supported from above, that 
is, if it be suspended from a fixed point, hang- 
ing freely, the centre of gravity will always 
settle in a vertical line beneath the point of 
suspension. 

128. The exact situation of the centre of 
gravity must depend partly on the figure and 

partly on the uniform or varying density of the whole mass of any 
body. Suppose a body to be of uniform density throughout, its 
centre of gravity may be experimentally ascertained by balancing 
it on the edge of a square table, in two positions, when the lines 
of equilibrium will intersect each other at a point over the centre 
of gravity, which manifestly must be in the centre of the mass. 
A body of small dimensions may be more accurately balanced on 
the edge of a knife ; or if the body can be conveniently suspended, 
and a plumb-line let fall from the point of suspension, its direc- 
tion being traced from two such points, will be found to intersect 
each other as before, at a point on the superfices which will indi- 
cate the situation of the centre of gravity. If a body varied in its 
density in different parts, and possessed considerable thickness in 
proportion to its length and breadth, holes bored through the mass 
in directions vertical to different points of suspension, would meet 
t the centre of gravity of such a body. 

of bodies result respectively from the support, and from the want of 
support to their centres of gravity ? 

Of what comparative length will a line be found, between the centre of 
gravity of a body and the point of its superfices on which it rests ? 

What relative positions will be found between the centre of gravity 
of a body and its point of suspension ? 

On what two circumstances must the position of the centre of gravity 
depend ? How can its situation be mechanically determined ? 





CENTRE OF GRAVITY. 67 

129. When the density of a body is uniform and its figure regu- 
lar, the centre cf gravity will be the central point of the mass ; as 
in a globe, an elliptical or oviform spheroid, or a parailelopiped. 

The surface of a triangle, its three sides, and its angular points, 
will all have the same centre of gravity, situated at two-thirds of 
the length of a right line passing from the vertex of the triangle 
to the middle of the base line. The centre of gravity of a cone 
will be at three-fourths of the length of its axis ; and that of a 
hemispherical solid at five-eights of the radius. 
A pyramid and its four terminating points will 
have the same centre of gravity. The figure of 
a body may be such that the centre of gravity 
will not be included within the mass. Thus a 
hollow cone, as a common extinguisher, or any 
body of similar shap^, would obviously have 
its centre of gravity in the void space within 
it ; and so would a basin-shaped body or hollow 
hemisphere. A piece of wire twisted into the form of a horse- 
shoe, or of a hoop, would also have its centre of gravity, not in 
the wire, but in the open space within it. 

130. The manner in which the centre of gravity of a body, 
when unsupported, tends towards the lowest point it can reach, 
may be illustrated by an amusing experiment, made with a piece 
of wood or any suitable substance turned in the shape of a double > 
cone united at the base, then if a jointed two-foot rule be opened 

a little way, and raised at the open end, so as to form a sort of 
inclined plane, the piece of wood on 
being placed at the bottom of the 
plane, will roll along to the raised 
extremity of the rule, seeming to 
ascend the inclined plane, passing 
as in the annexed figure, from A to B. This is, however, merely 
an optical deception, for the centre of the double cone, which 
must be its centre of gravity, really sinks lower and lower be- 
tween the sides of the rule as it advances to the open end. 

131. A somewhat similar experiment with an inclined plane, 
serves to show the effect of the different distribution of density or 
weight, in different parts of the moving bod)r. Suppose a cylinder 

to be made of light wood or cork, and to have a 
1 plug of lead passed through it from end to end, 
I so that its centre of gravity would be near its 
surface : if then it were placed on a moderately 
inclined plane with the loaded side towards the ascent, it would ne- 
cessarily turn till that side rested on the plane ; but it could plainly 
move no further, unless replaced, as in the marginal figure. 

Where will it be found in bodies of uniform density and regular figure ? 

How can you ascertain the centre of gravity in a triangle r a cone ? 
a hemisphere ? a pyramid ? Does the centre of gravity necessarily fall 
within the mass of every figure ? 

"What experiment illustrates the descent of the centre of gravity when 
unsupported ? What one exhibits the influence of distribution of density.'' 




68 



MECHANICS. 



132. The necessity of supporting- the centre of gravity in every 
situation appears from the manner in which we move in the act 
of rising from a seat. When a person is sitting- the centre of 
gravity of the body will be supported by the seat, from which it 
will be impossible to rise without bending the body forward so 
as to bring the centre of gravity over the feet, previously to as- 
suming the erect position ; or else lifting the body by resting the 
hands on the back or sides of the seat or some other point of sup- 
port. The utter incapability of locomotion that takes place when 
an animal is so situated that it cannot by its own efforts raise the 
centre of gravity of its body, is strongly exemplified in the case 
of a fat sheep, or ewe with lamb, which has been so unlucky as 
to lie down on the border of a shallow ditch or trench in a field, 
and roll over on its back into the hollow, where, in spite of its 
utmost efforts, it would lie with its feet in the air till it perished 
with hunger, if not assisted to rise. A tortoise thrown on its 
back affords another striking example of the same kind ; in this 
manner sea turtle are captured on shore. 

133. From what has been stated it is evident that the stability 
of a body must be increased by lowering its centre of gravity. 

A cylindrical vessel A B, suspended by a handle 
/""' "^\ turning on pivots fixed near the bottom, would in- 
evitably overset when empty, as the centre of gravity 
C would then be above the points of suspension ; 
but if a very heavy substance as quicksilver, or 
steel-filings, were poured into it, so as to fill it to 
the line D E, the centre of gravity would be re- 
•° duced to F, and the vessel might be suspended with 

safety. Hence it may be perceived why vans and stage-coaches, 
if heavily loaded at the top, will be very liable to be overturned, 
while a similar or greater weight placed low down will prove a 
security from danger; and on this 
principle " safety coaches" have been 
constructed, with receptacles for heavy 
luggage under the bodies of the vehi- 
cles. 

134. The effect of placing the 
centre of gravity of a body in a very 
low situation is shown in vibrating 
figures, such as that represented in 
the margin, and other toys for the 
amusement of children, formed on 
similar principles. Thus likewise a 
long stick or ruler, placed loosely on 
a bench or table, with more than half 
its length projecting beyond the edge of the board, may be made 

How is the position of centre of gravity illustrated in the manner of 
rising from a seat ? How is its importance shown in the positions of 
animals ? What effect on the stability of a body has the depression of 
its centre of gravity? What familiar applications can be adduced ? 




OF SUPPORTING THE CENTRE OF GRAVITY. 



69 




to support a bucket of water or a half hundred weight suspended 
on it. The manner in which this is ef- 
fected will be easily comprehended from 
the annexed figure, in which let A B 
represent the stick, which must have a 
notch or noose at the end B, against which 
rests another stick or prop, and the handle 
of the bucket being suspended by a string- from the first stick, the 
prop pressing- against the string at its junction with the handle 
C, fixes the bucket in such a position that the greater part of its 
weight and consequently the centre of gravity of the whole ap- 
paratus is supported by the table ; and therefore, so long as the 
parts remain connected, the equilibrium will be preserved, for the 
end of the stick B cannot be depressed without raising the centre 
of gravity. A common tobacco-pipe, in the same manner, may be 
made to sustain any weight short of that which would completely 
crush it. 

135. As a body of any kind cannot retain its position unless its 
centre of gravity be supported, it follows that stability may be 
preserved so long as a line directed from that centre vertically 
towards the surface below falls within the polygon formed by the 
base of the body in question. Hence the broader the base of any 
body the more securely will it stand ; and on the contrary when 
the base is extremely narrow a body will easily be thrown down. 
If a portion of any mass overhangs its base, it may still remain 
standing so long as the vertical line from the centre of gravity 
falls within the base. Thus a column, an obelisk, or a steeple 
might incline somewhat from the perpendicu- 
lar, and yet stand firm. From the inspection 
of the annexed figures it will appear that the, 
inclination of a column might be greater 
than is represented in the first figure, where 
the line A B falls within the base, without 
endangering the stability of the body ; but 
it must be less than that in the second figure, 
where the corresponding line C D falls with- 
out the base. 

136. Most very lofty buildings swerve in 
some degree from the perpendicular after a time, yet there can be 
no hazard of their destruction if properly erected. The monument 
built by Sir Christopher Wren, near London Bridge, to comme- 
morate the great fire in 1666, and the elevated spire of Salisbury 
Cathedral, have both become slightly inclined, but they will pro- 
bably long remain to afford standing evidence of the consummate 
skill of their respective founders. Travellers have frequently no- 
How do vibrating figures exemplify the position of centres of gra- 
vity ? 

What advantage does an extended base afford for preserving the sta- 
bility of bodies^ What examples prove that leaning bodies may some- 
times have a stable position ? 




70 MECHANICS. 

ticed the leaning- towers of Bologna and Pisa, especially the latter 
which is one hundred and thirty feet high, and inclines so much 
that the summit overhangs the base fifteen or sixteen feet; yet 
the line of direction from the centre of gravity dropping within 
the base, the structure has continued to stand or rather to lean for 
some centuries, and will probably endure centuries longer. 

137. A change of the position of a body which leaves its centre 
of gravity unsupported, must necessarily destroy its stability. 
Hence a high carriage is liable to be overset when one side is 
raised more than the other by the wheels passing- over a bank or 
by the sloping direction of the road ; and an over-freighted boat 
may be capsized somewhat in the same manner, by a sudden lurch 
throwing the weight on one side. Such an accident may like- 
wise happen in consequence of a person incautiously rising when 
a boat inclines to one side, the situation of the centre of gravity 
being thus altered, so as to swamp or upset the boat. 

138. The impossibility of preserving any position without 
keeping the line of direction of the centre of gravity within what 
may be termed the area of stability, or polygonal surface by 
which the body is supported, may be experimentally illustrated 
by observing the effect of placing- a person to stand with his heels 
close together and in contact with a perpendicular wall; for with 
such a position of the feet it would be found that he was unable 
to stoop sufficiently to touch the floor with one hand. The act of 
stooping is performed by bending the lower part of the body 
backward while the upper part is inclined forward, and thus 
though the situation of the centre of gravity is lowered, its line of 
direction still falls vertical^ between the feet. Now a person 
with his heels and of course his back also against a perpendicular 
wall could not possibly bend backward, and in attempting to lean 
forward he would inevitably lose his balance and fall down. So 
that one might scatter a handful of silver or gold on the floor be- 
fore a person stationed as just described, and offer him all that he 
could pick up, while he kept his feet unmoved, without the 
slightest risk of losing one's money. For the sake of any one 
who might choose to try the experiment it should be remarked 
that the terms specified must be strictly adhered to ; for if the 
heels are raised so that the body is supported by the toes, it will 
no longer be impossible to stoop sufficiently to touch the floor 
without falling : the requisite condition therefore should be that 
the heels must remain in contact with both the wall and the floor. 

139. A body will remain at rest, or in the state of equilibrium 
only in two cases, namely, when the centre of gravity is either 
as near as possible to the point of support, or as far from it as pos- 

What facts prove the importance of preserving the line of direction 
of a bod}' within its base ? What is meant by polygonal surface or area 
of stability ? What experiment shows the application of the principles 
of stability to the human body ? 

Under what two circumstances can the equilibrium of a body be pre- 
served ? 



^^^^^^ 



FEATS OF DEXTERITY. 71 

sible. In the former case, the stability of the body will be secure ; 
in the latter, extremely insecure; thus a heavy elliptical soHd laid 
lengthwise would require a considerable force to remove it from 
its place, but poised endwise the slightest impulse would cause it 
to roll over. When the centre of gravity is at the lowest point, 
a body is said to be in a state of stable equilibrium; and when it 
is at the highest point, in the state of instable equilibrium. 

140. Many feats of dexterity, as walking on stilts, dancing on 
the tight rope, standing on a slack wire, and balancing bodies either 
in motion or at. rest, depend chiefly on the power of maintaining 
the state of instable equilibrium. Walking on stilts, sometimes 
practised by school-boys, as an amusement, is adopted as a mat- 
ter of convenience by the shepherds in a district called the Landes, 
in the south-western part of France. The country there being a 
sandy level sometimes covered with water, the shepherds on 
leaving home take their lofty stilts, and may be often seen strid- 
ing along, on their artificial supports, at an immense rate. The 
art of rope-dancing is facilitated by holding in the hands a long 
pole in a transverse direction ; for a trifling elevation of one end 
of the pole and consequent depression of the other may be made 
at any time, to prevent the lateral deviation of the centre of gra- 
vity from its proper position vertically above the rope. Standing 
or walking on the slack wire appears to be a more arduous feat, 
than moving on the tight rope; yet it is practised merely by keep- 
ing the arms extended to preserve the equilibrium ; and some- 
times in that attitude the performer will make a further display 
of skill, by balancing bodies, one above another, on his chin. 
Occasionally an exhibition of dexterity on the slack wire is made 
to appear more difficult, by the performer having handed to him a 
chair, and a small table which he fixes across the wire, by rest- 
ing on it the rails which connect the legs of the chair and of the 
table, then seating himself in the chair and placing his feet above 
the front rail of the table, he keeps the whole accurately equi- 
poised even when the wire is made to swing from side to side. 
But though this feat has a more imposing effect than standing 
alone on the wire, there is no doubt that it may be performed with 
greater facility; for the table, and in a less degree the chair also 
serve, like the pole in the hands of the rope-dancer, to assist in 
maintaining the centre of gravity in its proper place. 

141. These feats, curious as they are, appear much less won- 
derful than the exhibitions described by some ancient writers 
of respectability, in which elephants are represented as walking 
on a tight rope. The difficulty of preserving the centre of gravity 
of so unwieldly an animal, moving on such a narrow line seems 

How do we distinguish the two states of stable and unstable equili- 
brium ? What feats of dexterity refer to the conditions of equilibrium 
for their explanation ? 

AVhat remarkable feats are related to have been executed on the same 
principle by quadrupeds ? 



72 MECHANICS. 

nearly to approach impossibility; but the evidence of the fact ap- 
pears to be deserving of credit.* 

Mechanic Powers. 

142. Nature presents to our notice force capable of producing 
motion, under various modifications. The weight of solid bodies, 
the impulse of flowing water, the pressure cf currents of air, the 
musculaT exertions of men or brute animals afford familiar exam- 
ples of different kinds of forces or means of originating motion ; 
and it is the peculiar province of mechanical science to supply 
rules for the accumulation, distribution, application, and expendi- 
ture of these or any other forces, in the most advantageous man- 
ner, by means of machinery. 

143. In investigating the effect produced by any machine, there 
are three things to be considered : 1. The nature of the force ap- 
plied, generally styled the power ; 2. The force opposed to it, 
called the resistance ; and 3. The point or points of connexion 
between the power and the resistance, which when there is only 
one point, as in the most simple machines, may be termed the 
centre of action, and where there are two or more such points, the 
action of the antagonist forces must be distributed over those 
points. 

144. Weight being in itself one of the most efficient kinds of 
force, and at the same time a common property of all bodies to 
which force can be applied, it has been very properly adopted as 
a convenient measure or medium of comparison of moving forces 
in general. But as the mere weight of a body in motion can 
afford no just indication of its impulsive force, the term moment 
or momentum has been adopted to denote the absolute force of a 
moving body with reference to the effect it is capable of produc- 
ing. The difference between the force of a body at rest and that 
of the same body in motion, that is between its weight and its 
momentum, in different circumstances, will be obvious on the 
slightest consideration. Thus a musket-ball which might not he 
heavy enough to break through a sheet of tissue-paper, when laid 
gently on it, would perforate a much firmer substance, if dropped 
on it from a considerable height, and fired from a gun it would 
penetrate a thick deal board. The momentum of a body then must 
be estimated by its weight and velocity taken together. 

Enumerate some of the natural forces capable of producing motion. 
What has mechanical science to do with these forces ? 
How many and what things require to he considered in examining the 
ffect of a machine ? 
What is meant by the term centre of action? 
What is the difference between force and momentum ? 



* " Notissimus Eques Romanus elephanto supersedens per catadro- 
mum, id est funem, decurrit." — Suetonius in Vita JVeronis. References 
to other writers, ancient and modern, who have noticed the exhibitions 
of elephants on the tight rope, are given in Beckmanii's Hist, of Invent. 
Eng. Tr. vol. iii. p. 311. 



THEORY OF THE MECHANIC POWERS. 73 

145. From what has been stated elsewhere, it may be inferred 
that any force which would drive a body weighing two pounds a 
given distance in one minute, would drive a body weighing but 
one pound twice as far in the same time ; and hence the velocit}*- 
of the latter body would be double that of the former, though both 
impelled by the same force. Both bodies also would have the 
same momentum, as will appear on multiplying the velocity of 
each body respectively by its weight : for the velocity of the nrst- 
mentioned body may be represented by 1, and that of the last- 
mentioned, being double the other, hy 2 ; then 2lb. X 1 = 2, and 
lib. X 2 = 2. And the same result will be obtained if we take 
the whole distance passed through by each body in a given time 
as the measure of its velocity ; for suppose the body weighing 
two pounds to run a quarter of a mile in a minute, and that weigh- 
ing one pound half a mile in the same time ; then i m. = .25 x 2 
=50, ^ m. = .50 X 1 = 50 ; the sum expressing the momentum 
of either body being the same. Since the momentum of a moving 
body is to be estimated by its weight multiplied into its velocity, 
it follows that a comparatively small body may by the celerity of 
its motion produce a much greater effect than a body of far supe- 
rior bulk moving slowly. Suppose the weight of a battering ram 
(such as was anciently used in war), to be 20,000 pounds, and 
that it moved at the rate of one foot in a second ; and the weight v 
of a cannon-ball to be 32 pounds, and that it moved 1000 feet in / 
a second, then the momentum of the former would be 20,000 X 

1 = 20,000, and that of the latter 1000 X 32= 32,000 ; and con- 
sequently the effective force of the cannon-ball would be more 
than half as great again as that of the ram, notwithstanding its 
immense superiority of weight. 

146. The mechanic powers are simple machines, or instru- 
ments, by means of which the acting force technically styled the 
power, is to be applied to the force which must be overcome, or 
that called the resistance. The advantage which is obtained by 
using these mechanical agents arises from the distribution of the 
resisting force among the different parts of the machine, so that 
the portion of it which is directly sustained or counterbalanced 
by the power bears but a small proportion to the whole ; and thus 
a power insufficient to communicate motion to a body or support 
its pressure, without mechanical assistance, may effect the pur- 
pose for which it is employed, by transferring a part of the weight 
to one or more of those points already noticed, whether it be the 
fulcrum of a lever, the wheels of a pulle}-, or the surface of an 
inclined plane. 

147. Different authors have varied considerably in the enume- 
ration of the simple machines or mechanic powers, from the 
combination of which and their several modifications all other 
machines, including those of the most complicated nature, are pro- 
Give some examples to illustrate this difference. 

What is the nature and what are the objects of the mechanic powers ? 
Under how manv general divisions mav all mechanic powers be classed ? 
G 



74 MECHANICS. 

duced. Considered as modes of the application of impulse to 
overcome resistance, all the mechanic powers may perhaps be 
most correctly arranged under three divisions: 1. The Lever; 
2. The Multiplied Cord; 3. The Inclined Plane. To these some 
have added the Wheel and Axle, the Pulley, the Wedge, and the 
Screw. But the wheel and axle is only a variety of the lever, the 
principle which regulates the action of both machines being pre- 
cisely the same. The pulley, so far as it possesses any distin- 
guishing property, must be considered as a multiplied coTd ; but 
in practice it is always used with wheels, and consequently it 
partakes in some degree of the nature of the lever. The wedge 
is nothing more than a double inclined plane applied in a peculiar 
manner, and acting exactly as a single inclined plane, but with 
twice the effect. The screw is a modification of the inclined 
plane, usually operating through the assistance of a lever. All 
these instruments have been commonly regarded as so many sim- 
ple machines ; it may therefore be as well to describe them 
separately, and in such order that the developement of their 
respective properties may illustrate the analogies among them 
which have been just pointed out. 

The Lever. 

148. The principle of action of all the mechanic powers is 
founded on the doctrine of equilibration, and is therefore intimate- 
ly connected with the theory of the centre of gravity, which has 
been already explained. As no single mass of matter can remain 
in the state of equilibrium unless its centre of gravity be support- 
ed, so any number of bodies connected together must have some 
common centre of gravity on which they will rest securely, if 
undisturbed, or oscillate round that centre, when impulse is ap- 
plied on either side of it. 

149. Suppose two balls of 
iron, A,weighing three pounds, 
and B,weighing but one pound, 
to be fixed to the opposite ends 
of an iron bar ; then whatever might be the length of that bar, 
(provided it was of equal diameter throughout,) the centre of 
gravity of the three connected bodies would be situated at a part of 
the bar just three times as far from the lighter ball as from th& 
heavier, the weight of the latter being three times as great as that of 
the former; and the bar being supported at that point the equilibrium 
would be maintained. Such a bar would be a kind of lever, with 
respect to which the large ball might represent the resistance, or 
force to be overcome ; the small ball the power applied ; and tbe 

To which of these does the wheel and axle belong ? to which the wedge 
and screw ? 

With what theory is the action of all mechanic powers connected ? 

What numerical relation exists hetween the length of the two arms of 
a lever and the forces applied at their extremities when in equilibrium ? 




THE LEVER. 75 

supporting- point the prop or centre of action, technically styled 
the fulcrum, which is a Latin word, signifying a prop. 

150. The mode of action of the lever may be further illustrated 
by observing - what takes place when two or more boys amuse 
themselves with a see-saw, or vertical swing. 

•e Here the plank A B forms 

jbILb a lever, of which the block 

^ sS ss== ssS jp\ C is the fulcrum, and in or- 

:n^ , m ^ a ^*= ssSS:S * 5S5 ^ • ^ er f° r ^ e pl an k to De equi- 

^Js^fx^-- I poised, it must be shifted 

•■jrbdf^^ jc\ ' -.. j into such a position that the 

— — ^ ' — : greater weight of the boy D 

nearest the fulcrum, may be compensated by the greater distance 
from that fulcrum of the boy E. 

151. Any number of boys might be placed at either side of the 
fulcrum, provided that the sum of the weights of all the boys on 
one side, multiplied by their respective distances from the fulcrum, 
were equal to the sum of the weights of the boys on the other side, 
multiplied by their distances respectively from the same point. 
Thuf, suppose the plank to be twelve feet long, and the fulcrum 
to be placed four feet from the end A, then a boy weighing thirty 
pounds at the end B would counterpoise another weighing sixty 
pounds at A ; or the same boy at B would support two boys weigh- 
ing forty pounds each, one being placed at A, and the other two 
feet nearer the fulcrum. This will appear from calculation, for 
the weight of the boy E, 30 X 8, his distance from the fulcrum, 
gives for the product 240 ; the weight of the boy D, 60 X 4, his 
distance from the fulcrum, also gives 240 ; and the weight of one 
boy at A, 40 X 4= 160, and another at two feet from the fulcrum, 
40X2 = 80, will by the addition of the products make 240. The 
plank being thus brought to a state of equilibration must, in order 
to make it vibrate, have some impulse given to it, either by the 
boys moving simultaneously upward on one side and downward 
on the other, and so on ; or by pressing alternately with their 
feet against the surface below, as either end preponderates ; or by 
any corresponding motion. 

152. It has been proposed to adopt the principle of the see-saw 
in the construction of machinery for economical purposes. In the 
Journal des Savans, June 13, 1678, an engine is described, by 
means of which cripples, if even deprived of their limbs, being 
placed on the extremities of a long lever, might, by the alternate 
inclination of their bodies in opposite directions, produce sufficient 
effect to work the pistons of pumps for raising water. And in 
the same journal a description is given of a vibrating quadrangu- 
lar frame, at one end of which four persons standing or sitting, 
might by their regulated efforts in depressing and raising the 

From what species of amusement may a familiar illustration of this 
truth be derived ? 

In what manner has it been proposed to apply the principle of the see- 
saw to useful purposes ? 



> 



7 6 :-i;:ckaxics. 

frame, eommimicatft a vertical motion to a saw for cutting timbei ; 
horizontal motion to surfaces tor polishing marble, or levigating 
powders ; force to a pair of shears for cutting through plates of 
metal ; or rotatory motion to a wheel for any purpose. * 

1% 153. Since the momentum of a body 

E . v ...--'"' \ is always to be estimated by its weight 

/ *\. g. ...--""'" \ and velocity multiplied together, and 

^rj— ~ j 3 the velocity by the space described by 

a moving body in a given time, it will 
follow that the momentum of bodies in 
a state of equilibration must be the 
w same. For let A B represent a lever 
kept in equilibrium by two leaden balls, the larger weighing two 
pounds, and the smaller one pound ; then suppose the weights 
were removed, the lever would take the direction E D, the ex- 
tremity A would describe the small arc A E, and the extremity 
B the arc B D, and those arcs would denote the spaces moved 
through by the respective ends of the lever. Hence the momen- 
tum of the two weights necessary to preserve the equilibrium of 
the lever may be found by multiplying the absolute weight of 
each by the number representing the velocity, or space described ; 
if therefore the arc B D be two inches, and A E one inch, it must 
be obvious that the products of the respective weights and veloci- 
ties multiplied together will in each case be two, which would 
express the momentum or moving force exerted by each weight 
to preserve the equipoise of the lever. It must also be noticed 
that the arc B D, or F D, will always be in a direct proportion 
to the line G B, and the arc A C, or E C, will bear the same pro- 
portion to the line G A ; so that, whether the number of pounds 
in each weight be multiplied by the number of inches in its 
corresponding arc, or by the number expressing its distance from 
the fulcrum, the result will show the momentum of both weights 
to be the same. For let G B be 12 inches, and G A 6, then 12 X 
1=6X2 = 12. 

154. A lever theoretically considered must be an inflexible rod, 
of uniform weight in every part, turning freely on a fixed point or 
fulcrum. There are three kinds or orders of levers: 1. That in 
which the power P and the resistance R act in the same direction, 
having the fulcrum F between them ; 2. That in which the power 
and resistance are in opposite directions, the latter being between 

What is meant by momentum, when applied to bodies at rest? Ex- 
emplify this in the case of the lever. 

What are the three characters of a lever assumed in theoretical inves- 
tigations ? 

How many orders of levers may be enumerated ? How are the seve- 
ral orders usually distinguished ? 

* This simple kind of machinery, known in French by the name of 
bascule, has been proposed for various other objects. — See Borgms 
Trait? des JMachhws. 



THE LEVER. 



77 



the fulcrum and the power ; 3. That in which the power and the 
resistance are also opposed, the former occupying the intermediate 
position, and being opposed to the fulcrum. 




155. In a lever of the first kind, those parts on each side of the 
fulcrum are termed the arms of the lever ; and the greater the 
relative length of that arm with which the power is connected 
compared with that to which the weight or resistance is attached, 
with so much stronger effect will the power be enabled to act. 
As the power will retain the lever in equilibrium when its mo- 
mentum is barely equal to that of the resistance, it must have a 
greater momentum in order to produce motion. Now its momen- 
tum or acting force, so far as it depends on the lever, is derived 
from the superior length of the arm with which it is connected ; 
and therefore in order to raise the weight or resistance, it must 
descend through a space as much greater than that through which 
the weight rises, as the length of the arm to which the power is 
applied is greater than the length of that arm to which the weight 
is appended. Thus by means of the lever, a small power can 
move a great weight ; but in this case the space passed through 
by the power will always be greater than that through which the 
weight moves ; and the greater the advantage which the power 
derives from the lever, the greater must be the difference of the 
lengths of its arms, and consequently the less will be the motion 
of the weight. 

156. A long lever turn- 
ing on a strong iron pin, 
as shown in the margin, is 
used by artillery-men to 
raise pieces of ordnance or 
other great weights. Wheelwrights and coachmakers employ a 
lever of similar construction, but having a shorter handle, and a 
higher fulcrum, and with this they raise a carriage on one side, 
when they want to remove a wheel. Crowbars and handspikes 
are levers of a similar kind, as also is the instrument called a 
jemmy, used by thieves, in breaking open doors or wrenching off 
locks or other fastenings. A pair of scissors, snuffers, or pincers, 
consists of two levers turning on a rivet, which serves as the ful- 

What are signified by the arms of a lever ? From what is the mecha- 
nical efficiency of the potver derived ? 

In what ordinary implements is the first order of levers exemplified? 
In what familiar example do the force and resistance act at right angles 
to each other ? 

g 2 




78 



MECHANICS. 



hich power is applied to overcome resist 



n 

*&- 

^ ii 



.-.c 




cruirj, on one side of v. 
a nee on the other side. 

A common claw-hammer may be employed as a 
lever, acting with considerable effect in drawing- out 
nails. In this case the line of direction of the power 
will be perpendicular to that of the resistance, as 
appears from the marginal figure. 

157. Here the advantage obtained by the power is 
to be estimated by its vertical distance from the ful- 
crum A C, compared with the horizontal distance C 
D, between the fulcrum and the resistance, represented by the 
weight B. When the power, or resistance, or both act ob- 
liquely, their effect will be diminished, according to the degree 
of obliquity. 

Suppose AB to represent a lever 
turning on a fulcrum at F, and let 
A R be the direction of the power P, 
and B S that of the weight W ; then 
if the line R A be continued to C, 
and the line S B to D, and the per- 
^ pendiculars F C and F D be drawn 
from the fulcrum to meet the lines of direction in the points C 
and D, the momentum of the power will be as its weight multi- 
plied by the number denoting the length of C F, and the momen- 
tum of the resistance will be as its weight multiplied by the num- 
ber denoting the length of D F. 

_ 158. Let B E be a curved 

lever supported at F, and having 
the power suspended at E, and 
the weight at B ; then the mo- 
mentum of the former will be 
found by multiplving its weighi 
by the line F G, or D E, and 
that of the latter by multiplying 
its weight by the line A F, or B 
G, are both shorter than the curve 
If the fulcrum F be in a straight line between 
B and E,this lever will possess the same character as if the lever 
were straight ; but if the fulcrum be situated out of a straight line 
while the force and resistance continue parallel, the lever will be 
progressive. This is the character of the bent steelyard, in which 
the poise being uniform, the weight is estimated by the height to 
which it will elevate the poise. 

159. Whatever may be the nature of the lever employed, as 
whether it be of the first, second, or third kind, its mode of action 
is in every case to be explained according to the principles already 

How is the advantage obtained by the poiver estimated when the direc- 
tions of the force and resistance are not parallel ? 

Describe the Lent lever. How may the mode of action of all levers 
ge explained ? 




C. These lines 
arms of the lever. 



THE LEVER. 79 

laid down. Thus in a lever of the second kind, in which the 
resistance, or weight to be overcome, is placed between the ful- 
crum and the power (see 154), the advantage of the latter 
will be increased in the same ratio, as that of the distance or 
space between the power and the fulcrum to the space between 
the resistance and the fulcrum. 




'60. The annexed figure (1) represents the manner of using a 
handspike or bar as a lever of the first kind : (2) shows how a 
similar bar may be employed as a lever of the second kind ; the 
point of the lever here being fixed against the ground or surface 
below the body to be moved, and the power applied to the oppo- 
site end of the lever. Among the various examples which might 
be adduced of levers of the second order, may be mentioned the 
knife used by druggists for chipping sassafras, quassia, and other 
medicinal woods ; one end being connected with a table by a 
hinge on which it moves as its fulcrum, the power is applied to 
the handle at the opposite extremity, and the substance to be 
chipped, forming the resistance, is placed between them, and is 
cut through by the edge of the knife pressing it against the table. 
The cutting blade used by chaff-cutters, and those of coopers, and 
last makers are likewise made to act on the principle of a lever of 
the second order. 

161. In rowing a boat, regarding it as the weight or resistance 
to be moved, the water must be considered as the fulcrum, against 
which the pressure of the blade of the oar, acting as a lever of 
the second kind, moved by the hand of the waterman, as the 
power, at the opposite extremity, produces the motion of the boat. 
A pair of nut-crackers is formed by two levers of the kind just 
described, moving on a hinge as a fulcrum ; and so likewise is a 
lemon-squeezer. When two men bear a weight on a hand-bar- 
row, one of them may be considered as occupying the place of 
the power, and the other that of the fulcrum. If they have both 
the same degree of strength, and can support the barrow in a 
horizontal direction, the weight or burden should be exactly be- 
tween them ; for if it be placed nearer to one than to the other, 
an advantage will be given to the man stationed furthest from it. 

162. In a lever of the third kind, (see 154) the power being nearer 
the fulcrum than the weight or resistance, the advantage lies on the 

What implement illustrates the second order of levers ? 

In what manner may we explain the effect of oars in rowing ? 

How are we to compute the relative portions of a given weight hornc 
by two persons on a pole ? 

How are the power, fulcrum, and weight arranged in a lever of the 
third order ? 




80 MECHANICS. 

side of the latter ; and therefore a greater degree of force would 
be requisite to support or move the weight by means of such a 
lever than that which would suffice to produce the same effect 
without the aid of any machine. But in this case the power will 
raise the weight through a greater space than that through which 
the power itself passes, and will consequently cause the weight 
to move with a velocity beyond its own. 
This will appear from the inspection of 
the marginal figure, in which the power 
P, acting over a pulley, from the point of 
the lever p, will, in moving the lever to 
the position F p W, raise the weight or 
resistance from w to W, while the power 
only passes through the space from p to p ; or more accurately 
the line described by the weight will be the arc w W, and that 
described by the point from which the power acts, will be the 
very small arc p p. 

163. This kind of lever therefore is not used to overcome great 
resistance, but either to move a weight with great speed, or from 
its peculiar adaptation to some particular purposes. Thus, a 
builder in raising a long ladder from the horizontal position, to 
place it against a wall, finds it convenient to fix the foot of the 
ladder against a block or stone, as a fulcrum, and laying hold^ of 
the ladder at half or three-fourths of its length, he supports at first 
the greater part of its weight, but gradually bringing it nearer 
and nearer to a perpendicular position, he shifts his hands accord- 
ingly from the point where he first grasped it, till he can bring 
them low enough to keep the ladder upright, and then it may be 
removed to the required situation. The treadle of a turning lathe, 
or grinding machine, affords a familiar example of a lever of the 
third order, in which* the pressure of the foot becomes the power, 
which, acting between the fulcrum and the resistance, sets the 
machine in motion. In a pair of tongs, or shears used in clip- 
ping the wool from sheep, two such levers are connected so as to 
have the fulcrum at the point of junction, and the hand in using 
one or the other, acts as the power between the fulcrum and the 
resistance. 

164. But the most interesting examples of the application of 
such levers may be found in the structure of animals. Thus the 
fore-arm, connected with the upper part of the arm by the elbow- 

' joint, moves on that joint as a fulcrum, the power that lifts or 
bends it being supplied by the contraction of muscles, acting from 
points between the elbow and the wrist. The whole arm is raised 
from the side of the body to a horizontal position in the same 
manner, chiefly by the action of a strong muscle called the Del- 

What sort of mechanical advantage is it the purpose of levers of the 
third order to attain ? 

What practical applications of this order of levers can be named ? 

What parts in the structure of animals exemplify the third order oi 
levers ? 



SYSTEM OF LEVERS. 81 

toid, forming the fleshy part of the shoulder, and stretching down 
on the outside of the arm, with the bone of which it is firmly 
connected. The bending- of the knee-joint and the hip-joint in 
walking, is performed by the corresponding action of strong mus- 
cles ; and in various parts of the human frame motion takes place 
in a similar manner. In the lower orders of animals an analo- 
gous kind of machinery may be discovered, as in the wings of 
birds, which are thus made to move with extraordinary velocity, 
that they may be enabled to act on a medium having so inconsi 
derable a degree of density as the air. 

165. Any number of levers may be connected together, so as 
to constitute a composition or system of levers, the power acting 
on the end of the first lever raising the end of the second, and 
that depressing the end of the third, so as to raise a weight at the 
opposite extremity ; or the alternate action may be continued 
through a great number of levers, the effect of which would be to 
augment vastly the momentum of the power, and to diminish in 
the same proportion the velocity of the weight, or resistance, so 
that the space through which that resistance would be moved would 
in general soon become very insignificant. The effect of such a 
system of levers must be estimated according to the relative dis- 
tances of the power and the weight respectively from the fulcrum, 
whether the levers were all of one kind, or some of one kind and 
some of another. 

166. Among the various applications of the lever, one of the 
most useful and important is in the construction of the common 
balance, styled, from its adventitious appendages, a pair of scales. 
The beam, which is the essential part of the machine, is nothing 
more than a lever of the first order, having equal arms, and turn- 
ing freely on its fulcrum, or centre of action.. It is hardly neces- 
sary to add, that its use is to ascertain the weight of bodies by 
equipoising them with an authorized standard ; and the principle 
on which this is effected has been already amply illustrated. 
There are however some circumstances requisite to insure the 
accuracy of a balance, which deserve to be noticed. 

167. The beam of the balance should be so formed that its 
centre of gravity may be placed just below the axis or centre of 
motion ; for if the centre of gravity and centre of motion coincided, 
it must be obvious that the beam would rest in any position in 
stead of assuming the horizontal direction necessary to indicate 
the equality of weights on each side. However, when a very 
delicate balance is required, its beam must be so constructed that 
the centre of motion may be as near as possible to the centre c r 
gravity, but somewhat above it. The extremities of the arms oi 
a balance are named the points of suspension, to which are fixed 
the scales ; and those points should be so situated that a straight 

In what manner may levers be combined together for the production 
of any desired effect ? 

How is the effect of such a system of levers to he estimated ? 

What circumstances are requisite to insure the accuracy of a balance? 



82 MECHANICS. 

line extending from one to the other would touch the point on 
which the beam turns. The sensibility of the balance is likewise 
influenced by the form of the fulcrum ; and in the most accurate 
balances the beam rests on a knife-edge moving on agate, polish- 
ed steel, or some very dense and smooth surface. Equal nicety 
is required in the suspension of the scales, which should hang 
from thin edges. 

168. Having thus stated the method of rendering a balance as 
exact as possible, it may be proper to notice some of the imperfec- 
tions of common balances, caused as they are too frequently by 
design, for the purpose of fraudulent deception. If the two arms 
be not precisely of the same length, the scale appended to the 
longer arm will turn with a less weight than that hanging from 
the shorter arm, and the purchaser of goods may thus be cheated : 
so also if one arm of the lever be heavier than the other, the scale 
on that side must preponderate. But deceptions of this kind may 
be discovered by changing the places of the weight and the arti- 
cle to be weighed ; for the lightest scale would no longer keep 
equipoised. And yet with such a pair of scales the true weight 
of a substance might be ascertained ; since by weighing it first in 
one scale and then in the other, multiplying together the two 
weights, and extracting the square root of the product, we should 
obtain the true weight.* 

169. The steelyard is another well-known kind of balance, 
more directly involving the principle of the lever in its construc- 
tion than the common balance. It consists of a lever with un- 
equal arms, turning on its fulcrum, and having on the longer arm 
a moveable weight, so that the body, whose weight is required, 
being suspended from the shorter arm, the equilibrium is attained 
by shifting the weight to the necessary distance from the fulcrum, 
and the longer arm being graduated and numbered, the weight 
appears from inspection. This is sometimes called the Roman 
balance, as alleged from its resemblance to the Roman statera ; 
though it has been stated that the original term was Romman, 
and that it was so called in the East, from the shape of the 
weight, resembling a pomegranate. f Such a balance as the steel- 
yard, but of small dimensions, and made of ivory or wood, is used 
by the Chinese for weighing pearls, precious stones, and other 
small objects. 

170. The Danish balance is a straight bar or lever, having a 
heavy weight fixed at one end, and a hook or scale at the other, 

What are some of the defects liable to be found in balances ? 
How ma)' a false balance be detected? 

How may the true weight of an article be obtained by means of such 
a balance ? 

How is the action of the steelyard to be explained ? 
What is the construction of the Danish balance ? 

* See Leslie's Elements of Natural Philosophy, vol. i. p. 186. 
t Idem, p. 187. 



THE WHEEL AND AXLE. 83 

with a moveable fulcrum, the situation of which indicates the 
weight of any substance which may be tried by it. The bar of 
course is graduated, and thus the weight may be determined, but 
the divisions becoming smaller in proportion as the weight in- 
creases, inconvenience occurs in ascertaining the exact amount 01 
the weight of very heavy bodies. 

171. The weighing-machine used at toll-gates on turnpike- 
roads, to discover the weight of loaded carriages, consists of a 
system of levers supporting a quadrangular floor. Four levers 
turning on their fulcrums extend from the angles of a box beneath 
the floor towards its centre where they are connected together, 
and also with another lever extending across the middle of the 
box, and passing beyond its limits ; this last lever acts on a third 
which presses on a spring or is connected with the arm of a ba- 
lance, by means of which the amount of pressure on the whole 
system may be ascertained. 

The Wheel and Axle. 

172. Though the lever may be considered as the most generally 
applicable, and consequently the most useful of all simple ma- 
chines, yet from the limited effect and intermitting action of power 
employed to overcome resistance by means of the lever, its grand 
utility must ever be confined to cases in which a momentary effort 
is required to change the place or position of a body of a great 
weight, by the application of comparatively small power. Thus, 
if it be necessary to remove a heavy block of marble or granite 
from one place to another, and a lever can be applied in such a 
manner to one side of its base as to shift the position of its centre 
of gravity sufficiently to make the block turn over, it may thus be 
rolled to any given distance : but supposing the utmost effect of 
the lever be to raise the mass but one inch, or any space through 
which it would fall back to its first position, the lever alone would 
manifestly be quite useless. Hence different methods have been 
contrived for rendering the lever more effective, as by employing 
a German machine, called a Hebstock, by which the weight is 
propped or supported during the intervals between the successive 
operations of the lever; by the French machine, termed Roue de 
la Garosse, from the name of the inventor, and by means of which 
a lever is kept in a raised position by a ratchet wheel ; or by 
using the Universal Lever, which also acts by means of a ratchet 
wheel.* 

To what objection is it liable ? 

What is the construction of weighing machines for carriages ? 
What circumstance limits the utility of the simple lever ? How has 
it been proposed to obviate this defect ? 

* This kind of wheel can only move forwards or in one direction, be- 
ing prevented from turning the other way, by a spring detent falling be- 
tween teeth on its periphery. 



84 



MECHANICS. 




173. But these modes of operation must be nearly useless 
where it is requisite to raise a body to a great height, or move it 
through a considerable space, and for such purposes may be ad- 
vantageously employed the wheel and axle, sometimes called 
Axis in Peritrochio,* which has generally been ranged among the 
the simple machines, or mechanic powers, though it is in fact only 
a more complicated form of the lever, and it might with propriety 
be styled a perpetual lever. 

174. It consists of a wheel or large flat cylinder, with a smaller 
cylinder passing through its centre, as an axle, to which it may 
be fixed so as for both to move together about the same centre, 
or the wheel may turn on its axle, in which case the effect will 
be different from that where the parts of the machine are con- 
nected. 

In investigating the operation of the wheel 
and axle both parts must be considered as 
turning on a common centre. Let the an- 
nexed figure represent a horizontal axle, rest- 
ing at its extremities on pivots, or supported 
by gudgeons, so that it may revolve freely, 
carrying round with it the attached wheel. 
On the axis is coiled a rope which sustains 
the weight; and round the periphery of the wheel is coiled ano- 
ther rope, in a contrary direction, to which is suspended the 
power. Then supposing the machine to be put in motion, the 
velocity of the power will be to that of the weight, as the circum- 
ference of the wheel to that of the axle ; for it will be perceived 
that the power must sink through a space equal to the circumfe- 
rence of the wheel, in order to raise the weight through a space 
equal to the circumference of the axle. And as the momentum 
of any body may be found by multiplying together its weight and 
its velocity, it follows that if the number of inches in the cir- 
cuit of the wheel multiplied by the number of pounds in the 
power, produce a sum equal to the product of the measure of the 
axle multiplied by the number of pounds in the weight, then the 
power and weight will remain in equilibrium. 

175. As before stated, the momentum 
of bodies moving in circles will be as the 
j-a products of their weights and the radii 
of the circles they respectively describe, 
therefore when the power bears the 
same proportion to the weight as the ra- 
dius CD or the diameter F D of the axle does to the radius A B or 
the diameter E B, of the wheel, the machine will preserve the equi- 




What name might properly be applied to the wheel and axle ? Ot 
what does it consist ? In what ratio are the power and weight to each 
other when this machine is at rest ? 



* From the Greek Ajr«», an axis, and ihpti 



to turn round. 



THE WHEEL AND AXLE. 



85 




librium ; so that the effect of this machine will depend on the supe- 
riority of the radius, or diameter of the wheel to that of the axle. 

176. The wheel may be moved by a weight acting on its peri- 
phery, as already described ; by projecting pins, or by a bent han- 
dle, such as is used for the common draw-well ; but whether the 
power be applied directly to the circumference of the wheel, to 
the extremities of the projecting pins, or to the handle, its effect 
must be estimated by the extent of the circle described. 

177. That the wheel and axle differs not 
in principle from the lever may be demon- 
strated from considering the effect of a sin- 
gle wheel used not for the purpose of in- 
creasing power, but merely in order that a 
power may be enabled to act in some re- 
quired direction. For let C be any weight, 
as ten pounds, suspended over a wheel by 
a line held at D, it will be obvious that 
setting aside the effect of friction, a power 
1^ equal to ten pounds must be applied to keep 
* "" the weight equipoised. Now the pivot on 
which the wheel turns will manifestly be the centre of motion or 
fulcrum, supporting the joint action of the poAver and the weight; 
and the lines A E and B E will represent the equal arms of a le- 
ver held in equilibrium, like a balance loaded with equal weights. 
178. A Venetian window-blind is usually suspended in this man- 
ner, by an endless line passing round two wheels ; and while both 
sides of the line are equally stretched, the blind will remain at any 
height, but destroying the equilibrium, by pulling the line on one 
side or the other, will raise or lower the blind at pleasure. In the 
wheel and axle the radius of the wheel represents the longer arm of 
a lever, and the radius of the axle the shorter arm ; and hence the 
advantage this machine affords. And as its action may be con- 
tinued indefinitely, each revolution producing an uninterrupted 
effect, the power may be regularly applied till the object in view 
be attained. 

179. One of the most efficient forms 
of the wheel and axle is displayed in 
the capstan used on board ships and in 
dock-yards. It consists of a vertical 
spindle fixed firmly as in the deck of the 
vessel, but turning on its axis, and sup- 
porting a drum, or solid cylinder con- 
nected with it, and having its periphery 
pierced with holes directed towards its 




On what will the effect of the wheel and axle depend? How is the 
effect of the wheel to he estimated', when the cord is not applied directly 
to its periphery ? Hpw can you prove the identity of the wheel and 
axle, and the simple lever ? Of what practical applications is this machine 
susceptible ? What is the construction of the capstan, and how is its ef- 
fect to be computed ? 

H 




86 MECHANICS. 

centre. It is then worked by long levers, inserted in the holes 
by men who walk in succession round the capstan, and thus make 
it revolve, while a rope or cable wound about the spindle may act 
with force sufficient to weigh a ponderous anchor, or warp a heavy- 
laden vessel into harbour. 

ISO. The treadwheel is anothor modification of the wheel and 
axle, in which the weight of several per- 
sons stepping constantly at the circumfer- 
ence of a long wheel make it revolve by 
their weight ; as may be readily compre- 
hended from the annexed figure. A some- 
what similar wheel turned by the weight 
of one man is used in Persia and some 
other oriental countries, for raising water. 
One or more horses may be made to work a mill, by harness- 
ing them to the extremity of shafts or lon<r levers fixed to an axis, 
which they turn-round by walking in a circle ; as in a machine 
for triturating clay for brick-making, and in some malt-mills. A 
treadwheel of a peculiar form is used in some parts of the United 
States acted on by horses, oxen, or other animals. 

181. The axle of a wheel sometimes has a conical or tapered 
shape, which affords an advantage when a varying force is to be 
overcome. The mainspring of a watch, the power of which is 
employed to uncoil a chain, acts thus on an axis, called the fusee, 
on the surface of which is cut a spiral groove to receive the chain ; 
and when the watch is newly wound up, the spring acts with its 
greatest intensity to turn the fusee while the chain passing round 
that part where the diameter is shortest, affords but a small lever- 
age ; and as the elastic force of the spring gradually diminishes 
by its relaxation, it obtains greater and greater purchase by the 
increasing diameter of the fusee as the chain is uncoiled ; so that 
by this means an equability of action is maintained, without 
which the watch would be useless. A similar contrivance is 
adopted to equalize the effect of power applied in raising ore from 
a deep mine ; for the rope, when at its greatest length, (and con- 
sequently when the resistance of the weight is greatest), is coiled 
about the narrow end of the axle, and the successive coils advance 
towards the wider extremity, as the resistance diminishes by the 
shortening of the rope. 

182. As the efficiency of the wheel and axle, whatever may 
be its peculiar construction, is to be estimated by the ratio of the 
diameter of the wheel to that of the axle, it follows that increas- 
ing the former or diminishing the latter will augment the effect. 
Either method may be adopted to a certain extent ; but if the wheel 
be extremely large it may be inconvenient and unmanageable ; and 
on the other hand, if the axle be very slender, it will be w T eak 
and insecure. Both these evils are" avoided in the construction 

For what purpose is the treadwheel used in Persia ? 

What is the construction and advantage of the watch fusee ? 

How is the principle of the fusee applied in mining operations ? 



THE MACHINE OF OBLIQUE ACTION. 



87 




of the double capstan, an ingenious 
contrivance, said to have been brought 
from China. It consists of two cylin- 
ders differing in diameter, connect- 
ed, as in the marginal figure, turn- 
ing about the same axis, while the 
weight is suspended by the loop of 
a long cord, one end of which un- 
coils progressively from the smaller 
cylinder, as the other laps round the 
larger: thus the weight is elevated at 
each revolution through a space equal 
to half the difference between the cir- 
cumferences of the two cylinders. So that the mechanical ad- 
vantage of the machine, with its pulley, will be in the ratio of 
the diameter of the larger cylinder to half its excess above that 
of the smaller one ; and therefore the equilibrium will be preserved, 
when the product of the power multiplied by the former is equal 
to that of the weight multiplied by the latter. This is true when 
the machine is moved by a hand rope applied to the larger cylin- 
der; but when the crank is employed, twice its length must be 
substituted for the diameter of the larger cylinder. 

183. The efficiency of wmeel-work may also be indefinitely 
augmented by a system or composition of wheels and axles, as in 
the case of the lever Thus the effect of the power that acts at 
the circumference of tne first wheel may be transmitted to the 
circumference of its axle, with which a second wheel being con- 
nected may act through its axle on a third wheel, and so on to any 
given extent. One wheel may be made to turn another merely 
by the friction of their surfaces, when but little force is required ; 
but the most direct and accurate method of connecting trains of 
wheel-work is by teeth or cogs, on the peripheries of the wheels ; 
and on this principle a great variety of complex machines are con- 
structed. Different wheels may also be connected by a strap or 
band, as is the case with spinning-wheels and the wheels of turn- 
ing-lathes. 



The Machine of Oblique Action, or Multiplied Cord. 

184. To this kind of mechanic power may be referred all those 
cases in which force is transmitted by means of flexible cords or 
chains, from one point to another. It has also been styled the 
funicular system, but as including a variety of modes in which 
power can be applied by. means of inflexible rods or bars, as well 
as by flexible lines, to produce an equilibrium depending on the 



How is the double capstan, or differential axle, formed ? 
How much is a weight elevated by each turn of this machine ? 
How may the efficiency of wheel-work be augmented ? 
In how many methods may motion he transmitted from one wheel to 
another ? 



88 



MECHANICS. 




composition of forces, it might be, perhaps most properly, desig- 
nated the machine of oblique action. From the theory of the 
composition of forces, which has been elsewhere illustrated, it may 
be assumed that a force applied in the proper direction will balance 
any two forces ; but if one of these be sustained by some fixed 
point, the first force may be considered as acting only against the 
other ; and power may thus be indefinitely augmented. 

185. Suppose B N, N C, C O, and 
O B, to be four bars connected by 
joints or hinges at B, Nand 0, and by 
a spiral spring passing from the joint 
B, so as to unite it with the ends of 
the bars N C and O C at C. Pres- 
sure applied in the direction O N 
would elongate the spring with an effect which would increase 
in proportion to the decrease of the angle N C O, so that at the 
collapse of the bars B and C O into a rectilineal position, the 
effect would be incalculably great. 

186. If the end B of a pair of jointed rods be firmly fixed, and 
the extremity C made to act by pressure, as by a 
man pushing at A, the force at C, when the bars are 
brought nearly into a straight line may be equal to 
the weight of many tons. On this principle that 
part of the Russel printing-press is contrived by 
means of which the paper is applied to the t)^pes to 
take off impressions ; instead of using a screw turn- 
ed by a lever, as in the common printing-press. 
The same kind of mechanic power is employed for 
extracting the steel core from the hollow brass cy- 
linder used as a roller in the printing of cottons ; 
and various modifications of it have been adopted, 

with great advantage in several operations of art, where a vast 
momentary effort is requisite to produce a given effect. 

187. The theory of the machine of oblique action, as it applies 
to flexible cords, has been sufficiently explained in treating of the 
composition of forces. (See 35 & 3G.) It may, however, be here 
stated, that if a cord be acted on by equal forces in opposite direc- 
tions, its tension will be measured by one of those forces or 
weights, and must of course be uniform throughout; and what- 
ever flexures the cord may undergo, and however numerous be the 
fixed points it passes over, provided its motion be unimpeded, the 
weights required to keep it in equilibrium must be equal. But 
if a cord be fastened at one extremity and variously deflected, the 
effect of weights suspended to different parts of it will be modi- 




On what theoretical principle is the machine of ohlique action founded? 
Illustrate its application in the hinged apparatus or toggle-joint. 

How is this machine applied in the printing press ? 

For what species of effort is it peculiarly adapted ? 

What measures the tension of a cord stretched by equal weights at the 
extremities ? 



THE PULLEY. 89 

fied according to their situation ; so that a great weight acting 
near the point of suspension may be counterbalanced by a com- 
paratively small force at the opposite extremity of the cord. 



Tlie Pulley. 

188. This is rather a compound than a simple machine; for 
from the investigation of its nature and properties it will be evi 
dent that it is merely a combination of the wheel and axle with 
the multiplied cord ; and as the wheel, though a very useful, is 
not an essential part of the pulley, this machine may be regarded 
as a variety of the funicular system, or multiplied cord. 

189. The effect of a single pulley, or moveable 
wheel suspended by a cord from a hook at a fixed 
point, as in the annexed figure, will be to dimi- 
nish the resistance by one-half, so that a power 
equal to one pound will support a weight of two 
pounds. This must be manifest from considering 
that half the weight is supported by the hook, 
HI consequently the other half only is opposed to the 
|| jj-2 [j power. The same conclusion will be derived 

111 lU l from attending to the result of the action of the 




power in raising the weight; for double the length of rope must 
pass over the fixed pulley on the side of the power compared 
with that which passes over it from the weight; so that the power 
must descend two inches in order to raise the weight one inch. 
Thus the power will move as fast again as the weight, therefore 
its velocity must be double that of the weight, and its effect must 
be increased by such a pulley in the same ratio. 

190. The fixed wheel or pulley here, has no other effect than 
that of altering the direction of the power. (See 177.) Though 
a pulley might obviously be made to act without wheels, and the 
cord might be deflected by passing through rings or by other 
means, so that the wheel must be considered as a sort of adventi- 
tious appendage to the pulley, yet, as already observed, it is an 
extremely useful one. For the wheel enables the cord to move 
freely, by destroying in a great measure the friction which would 
otherwise take place between the cord and* the surface over which 
it passes, and which would weaken, and in some cases interrupt, 
the action of the pulley. The wheels also serve the important 
purpose of keeping the deflected parts of the cord stretched in pa- 
rallel lines ; for the effect of the power would be diminished in 

When one extremity of a cord is fastened to an immoveable point, 
how will weights applied to intermediate points affect the cord ? 

How may the pulley be regarded in a theoretical view ? 

How are we to compute the effect of a single moveable pulley ? 

What is the effect of a single fixed pulley ? 

What is the advantage of the wheel in the construction of this ma- 
chine ? 

h2 



90 



MECHANICS. 



BaaggmsEESSa 




lib. 



any other position of the cord. Thus when 
the deflections of the cord form an angle, as 
represented in the margin, the power must be 
equal to more than half the weight, in order to 
keep the latter suspended; the machine will 
become less and less efficacious as the angle 
formed by the sides of the cord increases ; 
and when the two parts of the cord support- 
ing the weight approach nearly to a straight line, the power must 
be greater than the weight to enable it to preserve the equilibrium. 
191. In the pulleys just described, is ex- 
hibited the effect of the power when the 
weight is partly supported from one fixed 
point ; but that effect may be vastly augment- 
ed by such a system of pulleys as that in the 
annexed figure, in which the weight is sus- 
pended from the lowest of a series of wheels, 
each having its own cord attached to a fixed 
point. Here the resistance is diminished by 
the distribution of the weight over five fixed 
points ; so that supposing the weight to be 
thirty-two pounds, the wheel A, with its cord, 
will support the whole of that weight ; the 
wheel B, with its cord, half the weight or 
sixteen pounds ; C, one-fourth of the weight 
or eight pounds; D, one-eighth or four pounds; 
E, one-sixteenth or two pounds, which being 
divided by the two sides of its cord, leaves 
but one pound to be supported by that side 
which is extended over the fixed pulley F ; and 
thus a power equal to one pound will counter- 
balance a weight of thirty-two pounds. 

192. When one cord only is used, which 
passes over two or more fixed and moveable pul- 
leys, the power will be to the weight, as unity, 
or the single part of the cord supporting the 
power, to the number of the deflections made by 
the cord in passing over all the fixed and move- 
able pulleys. Hence if the power be augmented, 
so as to raise the weight, the former must de- 
scend through as many inches more than the 
latter ascends, as the number of bends in the cord 
supporting the lower block exceeds unity: that 
is, the power must sink four inches or feet to 
elevate the weight one inch or foot ; and such 
will be the ratio of its efficiency with such pul- 
leys as that shown in the marginal figure, the 
advantage gained depending on the number of 
wheels and consequent deflections of the cord. 

How does the obliquity of the cords affect the relation between the 




321bS. 



THE INCLINED PLANE. 



9) 



193. A great variety of systems, or, as they 
are commonly termed tackles of pulleys, have 
been contrived ; but the advantages they respec- 
tively afford may always be estimated by refer- 
ence to the spaces relatively described by the 
power and the weight or resistance. The great- 
est inconvenience occurring in the practical ap 
plication of the pulley, is owing to friction, and 
consequent irregularity of action. Various plans 
have been adopted to remedy this defect ; one of 
the most ingenious of which consists in cutting 
a proper number of concentric grooves on the 
face of a solid wheel, with diameters, as the odd 
numbers, 1, 3, 5, &c, for the lower block, and 
corresponding grooves on another such wheel, 
with diameters, as the even numbers, 2, 4, G, 
&c, for the upper block. Then the cord being 
passed in succession over the grooves, as repre- 
sented in the margin, it will be thrown off by 
the action of the power, in the same manner as 
if every groove formed a separate and independently revolving 
wheel. A machine of this construction is called White's pulley, 
from the name of the inventor, Mr. James White, who obtained a 
patent for it. 

194. Tackles of pulleys are used on board ships, where the 
wheels are fixed in blocks, by means of which the sailors can 
raise the masts, hoist the sails, and conveniently perform other 
necessary operations. Various combinations of pulleys are like- 
wise used on land, as by builders, in raising or lowering great 
weights ; and in removing from one level to another heavy bales 
of goods, or other merchandize. v 





The Inclined Plane. 

195. This is the least com- 
plicated of all the simple 
machines. It is, as the name 
implies, a plane surface, sup- 
posed to be perfectly smooth 
and unyielding, inclined ob- 

power and the weight? How many times is the power multiplied by 
means of the system of attached cords and moveable pullies combined ? 
In what manner is the weight distributed among the cords in this ar- 
rangement ? How is the relation between the power and weight to be 
discovered when a single cord is combined with a system composed of 
fixed and moveable pullies ? 

In what general manner may the advantage of a tackle be computed ? 

What practical difficulty is encountered in the use of pullies with sepa- 
rate wheels ? How does White's pulley obviate this difficulty? Stale 
some of the useful applications of the pulley. 

What theoretical character is assumed in treating of the inclined 
plane? 



92 MECHANICS. 

liquely to a horizontal plane ; and its effect, as commonly used, is 
to diminish resistance, and thus enable a moderate power to sus- 
tain or overbalance a great weight. The mode of action of the 
inclined plane has been already fully explained (see 93 to 96), and 
the method of estimating - its efficiency, in any given case, may be 
readily comprehended by reference to the relative velocities of 
two bodies, one falling through a space equal to the vertical 
height of the inclined plane, and the other passing down its de- 
clivity. Suppose the height A B to be one foot, and the inclined 
surface A C to be four feet, then a weight of four pounds, W, 
resting on the plane, will be equipoised by a weight of one pound, 
P, hanging freely over a pulley. And as the inclined plane is 
commonly employed to facilitate the rolling or shifting of ponder- 
ous bodies from a lower to a higher level through a moderate 
space, its efficiency will be in the ratio of the length of the inclin- 
ed plane to its vertical height; thus with the machine just de- 
scribed, one-fourth of the force necessary to lift a great weight 
through the space A B, or the vertical height, would be sufficient 
to impel it up the declivity, from C to A. 

196. In this more than in most other machines great allowance 
must be made for the effect of friction, which must materially 
modify any calculation as to the advantage it affords. Instances 
of the application of the inclined plane to practical purposes so 
frequent! ) r occur, that it can scarcely be necessary to advert to 
them. Roads formed on declivities are a kind of inclined planes ; 
and railways are sometimes thus constructed, in such a manner 
that any weight, as a loaded sledge, may be made to ascend one 
plane or inclined railroad by the impulse of another carriage with 
which it is connected, and which passes simultaneously down 
an adjoining railroad. 

197. The very simple nature of the inclined plane renders it 
probable that it was the earliest of the mechanic powers known 
and brought into use. It has been conjectured that it was em- 
ployed by the Egyptians in raising the immense blocks of stone 
which form the pyramids, and in executing other gigantic works, 
which have excited the astonishment of successive ages. Mr. 
Warltire, a gentleman who delivered lectures on natural philoso- 
phy, in the latter part of the last century, endeavoured to prove 
that the ancient British Druids were the founders of Stonehenge, 
on Salisbury Plain ; and that they erected the massive trilithons, 
which partly compose that curious structure, by rolling or rather 
by shifting the transverse blocks into their places by means of 
temporary inclined planes of earth or rubbish, forming a sort cf 
road-ways for the passage of the several block. The annexed figure 



How is its mechanical efficiency estimated ? 

What familiar applications of the inclined plane may be enumerated ? 
What conjectures have been formed respecting its use among the an- 
cients ? 



THE WEDGE. 



93 



will afford a sufficiently accurate idea 
of one of the trilithons of Stonehenge, 
and when the structure was perfect, 
several of these were arranged in a cir- 
cular figure. It will not be difficult to 
conceive that a sloping bank or declivi- 
ty, having but a small degree of incli- 
nation, might be formed, up which any mass might be impelled 
or dragged, with a force not much greater than would be required 
to draw or push it forward on level ground. 





The Wedge. 

198. A wedge is the solid figure called by Geometricians a 
triangular prism, bounded on two sides by equal and similar tri- 
angles, and on the other three sides by rectangular parallelograms. 
It is composed of two inclined planes united at their bases ; as 

will appear from the annexed representation. Its 
use is to divide solid bodies, the edge E F being 
impelled against them by pressure or some other 
force applied at the surface ABCD; and if the 
force be estimated by its weight, its effect will be 
in the ratio of the line D F to the line G D, that 
is as the sides of the wedge to its breadth. So 
that the advantage derived from using this ma- 
chine increases in proportion as the angle which forms its edge 
diminishes. Bat the wedge is generally used for cleaving blocks 
of wood or other hard substances, and the force applied to it is 
that of percussion, with a heavy hammer or mallet, the effects of 
which are so different from those of direct pressure, and are so 
much modified by circumstances, as to render any theoretical cal- 
culation utterly inaccurate and useless. 

199. It. appears from the results of some experiments made in 
the Dock-yard at Portsmouth, England, on the comparative effect 
of driving and pressing in large iron and copper bolts, that a man 
of medium strength striking with a mall weighing eighteen pounds, 
and having a handle forty-four inches in length, could start or 
drive a bolt about one-eighth of an inch at each blow ; and that it 
required the direct pressure of 107 tons to press the same bolt 
through that space, but it was found that a small additional weight 
would press the bolt completely home.* 

200. But numerous and varied experiments would be requi- 
site to obtain any results which might afford data for computing 

What is the geometrical form of the wedge ? What relation has the 
advantage of this machine to the angle formed at its edge? Of what 
nature are the forces usually applied to the wedge ? 

What has experiment proved in regard to the difference hetween pres- 
sure and percussion ? 



* Encyclop. Metropol.- Mixed Sciences, vol.i. p. 5t 



94 MECHANICS. 

the effect of impact or percussion on wedge-shaped bodies ; 
and if that effect could be exactly estimated, further difficulties 
would arise from considering the very heterogeneous nature 
of the resistance, depending on the relative hardness, tenacity, 
and other properties of those substances on which the wedge is 
made to act. This instrument must therefore be regarded as 
one the effect of which can seldom be precisely determined ; but 
which notwithstanding may be often very advantageously employ- 
ed in certain circumstances. 

201. Among the less frequent modes of application of the wedge 
may be mentioned its having been used to restore to the perpendi- 
cular position a building which declined slightly in consequence 
of some defect in the foundation. The voussoirs of arches are so 
many wedges ; and piles used for the foundation of the piers of 
bridges may be considered as wedges, driven into the bed of a 
river by the percussion of a powerful machine. Sharp-edged and 
pointed instruments in general act as wedges'; thus chisels, planes, 
and axes used by carpenters manifestly produce the effect of 
wedges ; and knives, razors, awls, pins, and needles, and indeed 
all cutting and piercing instruments display an obvious analogy 
to the common forms of this mechanic power. 



The Screiv. 

202. The sqrew, though commonly reckoned among the me- 
chanic powers or simple machines, cannot be considered as such 
when applied to any practical purpose, as it would be found almost 
wholly ineffective without the assistance of the lever, which is 
therefore usually combined with it, and thus it becomes a most 
powerful machine, applicable to a variety of important purposes. 
The general form of the screw must be too w ell known to require 
description : it may however be stated, that it consists of two 
parts, namely a solid cylinder, sometimes called the male screw, 
and a corresponding cylindrical cavity, to receive the former part, 
and therefore styled a female screAv ; round the surface of the cy- 
linder passes what is termed the thread of the screw, describing 
from one end to the other a curve sometimes inaccurately represent- 
ed as a spiral, but which is really a helix, precisely resembling 
a common corkscrew, which, in fact, is nothing more than the 
helical thread of a screw without the core. The hollow screw 
has a similar helical thread winding within it, exactly adapted to 
the interyal between the turns of the thread of the solid screw ; 

Why is the actual effect of the wedge more difficult to be computed 
than that of other machines ? 

Of what applications is the wedge susceptible in the art of architec- 
ture ? 

Name some of the familiar applications of the wedge in ordinary in- 
struments. 

What is the nature of the screw in its practical structure ? 




THE SCREW. 'JO 

and thus either part being - made to revolve while the other is kept 
steady, motion or pressure may be produced to any extent.* 

203. In order to rbtain a correct estimate of the mechanical 
effect of the screw, it will be necessary to develope its construc- 
tion, from which it will appear that it is, in principle, identical 
with the inclined plane ; and it might be conceived to act as a 
system of revolving inclined planes. This will appear from refer- 
ence to the annexed figure. Let AB CD represent a c}dinder 
divided longitudinally into a number of 
equal parts, B a, a b, &c, and let lines a 
-e e, b f, &c, be drawn perpendicular to the 
-;p side A 13, each equal to the circumference 



=—y of the base ; then by joining B e, «/, b g, 
£ c A, will be formed so many right-angled 
triangles Bac, a bf, beg, c d A, as the 
number of equal parts into which the cy- 
linder has been divided. Now suppose 
these triangles to be rolled upon the cylin- 
der, so that the point e should coincide with 
the point a, /with b, g with c, A with d, and so on, the hypothe- 
nuses or longest lines of the triangles, B e, af, b g, c A, &c. would 
form on the surface of the cylinder one continued helical line, re- 
presenting the thread of a screw. These triangles might be con- 
sidered as a series of inclined planes; and therefore if such a 
screw w T ere fitted to a hollow or female screw, fixed so that the 
former might act vertically, it will be obvious that one revolution 
of the. male screw would raise or depress it through a space equal 
to the height of one of the inclined planes, and the effect of the 
screw, independent of friction, would be as the length of its 
base to its height, or as the line a e to B a. If then Babe | of 
an inch, and a e l^in. or 12-8, a power equal to one pound acting 
by means of the screw would balance a resistance equal to twelve 
pounds. The power must here be supposed to act parallel to the 
base. 

What is the distinction between a helix and a spiral ? 

How is an accurate estimate of the effect of the screw to be obtained ? 

With what other simple machine is its principle of action to be com- 
pared ? How much does one turn of the screw raise the weight or re- 
move the resistance ? 

* A spiral or volute is a line which can he described on a plane ; but 
no two points of a helix are in the same plane, and therefore it cannot 
be correctly described on a plane surface. 

Spiral Line. Helical Line. 




96 MECHANICS. 

204. But the resistance arising from friction between the parts 
of the solid arid the hollow screw would in most cases require 
n-reat additional power to produce any considerable effect. This 
therefore renders the application of a lever necessary to constitute 
the screw an effective machine. The lever may be added to the 
solid screw, to turn it within a fixed hollow screw ; or to the 
hollow screw, to turn it round the solid screw. The manner in 
which the lever is applied in either case will appear from the 
following- figures ; the former of which shows how pressure may 



C 





be produced by a solid screw acting; within a hollow screw in a 
fixed beam ; and the latter exhibits the similar effect of a hollow 
screw pierced in a block turning by means of a lever on a fixed 
screw ; the pierced block thus adapted to a solid screw is called 
a nut. 

205. As the effect of the screw is always to be estimated by 
the proportion between the space described by the power, in one 
revolution of the screw, and the space between any two of its 
contiguous threads, it must follow that when the power is appli- 
ed to a long lever instead of being made to act directly on the 
circumference of the screw, the effect must be vastly augmented. 
Thus if the threads of a screw be as much as half an inch apart, 
and it be turned by means of a lever extending three feet from 
the centre of the screw, the effect or advantage of such a machine 
will be as the number of half inches in the space described by the 
extremity of the lever to unity. Now reckoning the circumfer 
ence of a circle in round numbers to be three times its diameter, 
the circumference described with a radius of three feet will be 
36 x 2 = 72 X 3 = 216 inches, and double that number, or 432 
to 1 will be the measure of the advantage afforded by the ma- 
chine. 

206. Hence it will be apparent that the efficiency of the screw 
acted on by the lever might be indefinitely increased by extending 

Why is the addition of a lever necessary in this machine ? In what 
two modes may the lever be applied ? 

How is the effect of the screw to be estimated ? 

How far might the efficiency of the screw, theoretically considered, 
be increased ? 



THE COMPOUND SCREW. 



the length of the lever, or by diminishing- the interval between 
the threads of the screw. But a very long lever would be awk- 
ward and inconvenient, and extremely thin threads would be 
broken by the pressure when any considerable force was applied 
to turn the screw ; so that either method of improving its action 
could be practically serviceable only to a limited extent. There 
is, however, a kind of double or compound screw, invented by 
John Hunter, the celebrated surgeon, bearing much analogy to the 
double capstan or axle, already described, (see 182) by means of 
which the mechanical efficacy of the machine may be augmented to 
any extent without at all diminishing its strength or compactness. 
207. The marginal figure, which will show how this object is 
attained, represents a larger screw turning in a hollow screw or 
nut in the fixed beam, and having within it a 
concave screw adapted to the lower or smaller 
screw, and so arranged that while the larger 
screw passes forward the smaller one will be 
retracted ; hence as both screws must revolve 
together, in each revolution, the moveable beam 
will be pressed downward through a space 
equal to the difference of the distances between 
the threads of the larger and the smaller screws. 
Therefore such a machine, in which the threads 
of the upper screw were 1-20 of an inch apart, 
and those of the lower screw 1-21 of an inch, 
would have the same effect as a simple screw, 
the threads of w T hich were only 1-420 of an inch apart ; for 1-20 
— 1-21 = 1-420, the difference between the distances of the 
threads of the double screw just described. 

20S. A solid screw revolving on fixed axes, and having its 
thread adapted to teeth on the periphery of a wheel, is called an 
endless screw ; forming a part of a compound machine of consi- 
derable power and utility. Fly-wheels, as that of a common jack 
for roasting meat, are sometimes turned by the action of a toothed 
wheel on an endless screw. 

209. Besides its usual application to the purpose of producing 
a high degree of compression, as in the cider-mill, the common 
printing-press, and a variety of similarly acting machines, the 
screw is likewise employed to measure extremely minute inter- 
vals of space. The manner in which this object is attained will be 
best understood by referring to the theory of the screw, (see 205) 
where it is demonstrated that any circle described by an arm or index 




By what two expedients might this increase be effected ? 

What practical difficulties prevent the unlimited augmentation of the 
power of the screw ? 

What is the construction of Hunter's differential screw ? 

Through what extent does a single turn of this screw move the platen, 
of the press ? 

In what manner is the endless or tangential screw applied for mecha 
nical purposes ? 

I 



98 MECHANICS. 

revolving 1 parallel to the circumference of the screw will have a 
certain relation to the space between any two contiguous threads ; 
and therefore a small arc of such a circle may be conceived to 
measure the indefinitely minute space through which the point of 
the screw would advance or retreat in any given portion of one 
complete revolution of the screw. Suppose the threads to be } 
of an inch apart, and a circle fixed to the head of the screw to be 
divided on its border into 100 equal parts, then on turning the 
screw, the index would show the motion of the point of the screw 
through as small a space as 1-400 part of an inch. The interval 
between the threads of a screw for such a purpose might be ex- 
tremely minute, or Hunter's screw might be adopted ; and the 
circle of equal parts might be of sufficient extent to be divided 
into 360 degrees, or any larger number of parts ; and thus the 
means would be afforded for measuring- with perfect accuracy the 
almost invisible fibre of a spider's web, or for taking the dimen- 
sions of- the capillary vessels through which circulate the juices 
of plants and animals, or for discovering the size of microscopic in- 
sects or other objects too minute to be perceived by the naked 
eye. An instrument adapted to a microscope for such purposes 
is called a micrometer,* and its screw a micrometer screw. 

Compound Machinery. 

210. The advantage derived from combining together two of 
the mechanic powers, as the lever with the wheel and axle, or 
with the screw, has been already detailed ; and it is by means of 
combinations of the simple machines, under their various modifi- 
cations, that a vast multitude of complex machines are produced, 
which are adapted to facilitate the numerous operations required 
in the several departments of the arts, manufactures, and domes- 
tic economy. 

211. Among all the simple machines there is no one so gene- 
rally useful, and therefore so frequently making a part of com- 
pound machinery as that modification of the lever called the wheel 
and axle. Its advantageous adaptation to the purposes of the 
mechanist is partly owing to the nature of the motion to which 
it gives rise, namely rotation, which is capable of being uninter- 
ruptedly continued through a period of indefinite extent ; and to 
this advantage may be added the extreme facility with which 
wheels may be connected in various modes with other kinds of 
machinery. Hence there are few complex machines of which 

What is the construction and use of the micrometer screw ? 

On what are the divisions of a thread measured in a screw of this de- 
scription ? 

In what manner are the simple machines commonly adapted to the 
mechanic arts ? 

By what peculiarity is the wheel and axle rendered more serviceable 
to the mechanist than the other simple machines ? 



* From the Greek Mixaoc, little: and m=tcov, a measure. 



COMPOUND MACHINERY. 



99 



,o*D™^ 



wheels do not constitute the most effective or essential parts. 
Thus are formed a vast variety of mills, from the coffee-mill to the 
powerful and complicated engine called a rolling-mill, for com- 
pressing plates of iron and cutting them into rods or bars ; all the 
multifarious kinds of wheel-carriages ; turning-lathes, and grind- 
ing-machines ; clocks, watches, and timekeepers, in general ; 
spinning- jennies, and many other machines used in the cotton, 
linen, woollen, and silk manufactures ; and steam-engines under 
many of their modifications, to accommodate them to the purposes 
to which they are devoted. 

212. The peculiar methods in which the parts of machinery 
are connected, or the modes of action of one mechanic power upon 
another, or upon a different form of the same power, are variously 
diversified to suit particular purposes. The wheel and pinion, 
represented in the margin, consists properly of 
two wheels of unequal dimensions, the larger 
having teeth on its circumference which are adapt- 

O^ ed to correspondent teeth, or as they are some- 
f times called leaves, in the smaller wheel or pinion : 
thus a pinion may be made to act on a crown 
wheel, that is a wheel with teeth placed at right angles to its 
circumference ; as may be observed in a watch, or timekeeper. 
The endless screw is connected with the teeth of a wheel in the 
manner represented in the annexed figure. 

213. A little attention to the mode 
of action of many machines in con- 
stant use will afford opportunities foi 
observing numerous instances of the 
different ways in which trains of 
wheel-work are combined together, 
or made to aid the effect of the other 
mechanic powers. These are, how- 
ever, generally reducible to two me- 
thods of proceeding, namely, either 
by teeth, cogs, or some similar parts, 
acting against each other, as just 
described ; or by bands, as cords, 
chains, or other flexible lines passing wholly or in part round one 
or more wheels and axles, so as to produce simultaneous motion. 
214. With respect to the use of either of these methods, it is of 
importance to observe the peculiar nature of rotatory motion, which 
differs most essentially from what is termed a motion of translation, 
or passage from one place to another, though it may or may not 
accompany such a motion. Suppose any body, as a billiard-ball, 




Enumerate some of the applications of wheel-work. Describe the 
wheel and pinion. 

By what two methods is motion communicated from one part to an- 
other in a system of wheel-work ? 

How does a motion of simple rotation differ from one of transla- 
tion ? 



100 MECHANICS. 

a 33 l0 k e P usnec l fr° m A t0 B> ever} T particle of 

|||) f j the ball must have partaken of the motion ; 

but. if it be made to spin round in one place, 
the centre of the ball will remain unmoved ; for imagine such a 
ball, or a large globular bead to be pierced centncally, and have 
a wire passed through it, the ball might be made to revolve with 
any degree of velocity, while the wire was held perfectly steady. 

215. Let a circular disk of paper or any thin suDStance be made 
to revolve in this manner, on a pin, it will be 
perceived that the exterior surface of such a 
miniature wheel must move with greater ve- 
\\ locity than any other part; so that the point 
1 1 [ { o ) I A will pass over more space in each revolu- 

\\ \ '"• ■"' / // tion of the wheel than the point B; and the 

V\ *'••- .-•-' // latter over more than the interior point C. 

\N. .-^y Hence it must follow that every circle within 

the circumference of a revolving wheel will 
have a relative velocity corresponding with its diameter ; so that 
the degree of velocity communicated by a wheel in motion to some 
other part of a compound machine must depend not merely on the 
actual velocity of the wheel, but on that taken in conjunction with 
the relative distance from its centre at which the communication 
takes place ; whether it be by means of teeth, projecting pins, or 
cords running in grooved cavities. 

•216. When teeth are made the medium for the communication 
of impulse, their peculiar form requires attention ; but it can here 
only be generally stated that the teeth should be so constructed 
as to act upon each ether steadily, without jerking or rubbing, 
which would soon derange the machine ; and that the teeth most 
accurately adapted to produce the required effect, are such as have 
their corresponding surfaces forming peculiar curves, the exact 
figure of which in any case may be ascertained by geometrical 
construction.* 

217. It is likewise desirable that the teeth of one wheel should 
work successively in those cf the corresponding wheel, and that 
the same teeth should not meet in each consecutive revolution of 
the larger wheel ; as they will thus act more uniformly, and wear 
away more slowly than if the same teeth came in contact more 
frequently. This object is effected by making the numbers of 
the teeth of wheels acting together, or of a wheel and its pinion, 

How mav this difference be illustrated in the motions of a billiard 
ball ? 

By what will the velocity of motion of every circle in a revolving 
wheel be determined ? 

On what two circumstances in a driving wheel will the degree of ve- 
locity in the driven machinery depend? 

What circumstance requires particular attention in the construction of 
toothed wheels ? 

* See Leslie's Elements of jSTat. Philosophy, vol. i. p. 199 — 207. 



WHEEL-WORK. 101 

as discordant as possible ; so that the number of the teeth in the 
small wheel may never be an aliquot part of the number in the 
larger wheel. Thus, if a wheel of sixty teeth be turned by a 
pinion having - but ten, each of the latter would come in contact 
with the same teeth of the former in each of its revolutions, or 
in every sixth revolution of the pinion ; but if the larger wheel 
have sixty-one teeth, it must be manifest that no two corresponding 
teeth of the wheel and pinion respectively can meet more than 
once in every sixty-one revolutions of the pinion, during which 
the wheel will have revolved ten times. The odd tooth or cog 
by which this effect is produced is called by millwrights the 
hunting-cog. 

218. In the construction of complex machines, it is not merely 
requisite that they should afford the means of communication be- 
tween the power and the resistance, and enable the former to 
overcome the latter by the combined assistance of two or more 
of the mechanic powers, or simple machines ; but it also often 
becomes an object of the highest importance to change the di- 
rection of any given moving power or acting force, without which 
it may be utterly inapplicable to the intended purpose, and there- 
fore quite useless. 

219. Reciprocating rectilinear 
motion may be changed into 
circular motion, by a crank ap- 
plied to turn a wheel, as may 
be seen in the common knife- 
grinding machine, and in the 
turning-lathe ; and the same ef- 
fect is produced by what has 
been fancifully styled the sun 
and planet wheel, represented 
in the margin ; one wheel fixed 
at the extremity of a vertical 
rod which rises and falls alternately, acting by teeth on its peri- 
phery on a similar wheel to which it communicates a double ve- 
locity ; and thus the fly-wheel of a steam-engine was formerly 
made to revolve, but this method is now generally superseded by 
the crank. 

220. The opposite effect of curvilinear motion producing alter- 
nate rectilinear motion may be observed in the manner of working 
the pistons of an air-pump, or a fire-engine, as in the marginal 
figure below. A very ingenious contrivance for the conversion of 
rectilinear into curvilinear motion, or rather for producing an ac- 
curate correspondence between such motions, is displayed in the 

How is the irregularity of wear, from the frequent meeting of the 
same teeth in a wheel and pinion to be avoided ? What is meant by a 
"hunting cog?'''' 

How may reciprocating rectilinear motion he changed into circular 
motion ? 

How is curvilinear converted into rectilinear reciprocating motion ? 
I 2 




K2 



MECHANICS. 



system of jointed bars used to connect the piston-rods of the 
steam-engine and its air-pump with the great beam, whose reci- 
procating motion transmits the necessary force to the fly-wheel 
and other parts of the machine. A much clearer idea of the nature 
of this contrivance, termed the parallel motion, may be attained 
from inspecting a steam-engine at work, than from a detailed de- 
scription, even with the aid of a figure represent- 
ing its construction. 

221. The universal joint, invented by the cele- 
brated Dr. Robert Hooke, affords a simple and 
efficient mode of transferring rotatory motion from 
one axis to another in an angular direction; but 
this may be done with greater accuracy by means 
of beveled wheels, which, as will be understood 






from the foregoing figures may be made to act on each other ai 
any angle whatsoever. 

222. The regulation of the velocity or rate of motion is of the 
highest consequence to insure the efficiency of compound machine- 
ry. When two or more of the mechanic powers are made 
to act in concert, they must necessarily have certain points of 
contact ; and the material substances of which machines are 
constructed, being subject to variations of density and dimen- 
sions from the action of heat and cold, or other causes, regularity 
of action cannot be perfectly attained, unless some mode can be 
adopted to prevent the changes just mentioned from taking place, 
or to counteract their effects ; so that there may be such a stabili- 
ty in the points of contact of the mechanic powers, as to produce 
uniformity of combined action. Thus, in a clock or timepiece, 
uniform motion is propagated throughout trains of wheel-work, by 
means of a pendulum oscillating seconds ; and the pendulum there- 
fore acts the part of a regulator to the clock. 

223. In describing the pendulum and its peculiar kind of motion, 
it has been stated that to beat seconds it must have a certain 



What was the purpose of Watt's jointed bars, used in the construction 
of hi9 steam-engines ? 

For what purpose are beveled wheels applied in the construction of 
machines ? 

To what great purpose are regulators applied in the movements of 
machinery ? 



REGULATION OF MACHINERY. 



103 



length, corresponding to the latitude of the place of observation, 
or more strictly speaking to the distance of that place from the 
earth's centre. Now it has been discovered from observation that 
a pendulum-rod of brass, steel, or in fact of any substance adapt- 
ed for such a use, will be elongated by heat, and contracted by 
cold ; and that to such an extent by the common changes of tem- 
perature in the atmosphere at different periods, that a pendulum 
which would vibrate once in a second in the winter, would take up 
more than a second in performing one vibration in the summer ; 
and hence it would require to be shortened at the latter period, 
and lengthened again at the former to make it act with any tole- 
rable degree of uniformity. To regulate a clock in this manner it 
is obvious that the error must be observed before it could be cor- 
rected, and therefore this method though it might serve for com- 
mon purposes, would be nearly useless to the astronomer or the 
navigator, requiring a uniform and accurate measurement of a con- 
siderable period of time, by means of an instrument more or less 
exposed to alternations of temperature. The construction of a 
pendulum which should preserve its length unalterably in all 
situations, thus became an object highly interesting both to phi- 
losophers and mechanics ; and the contrivances which different 
individuals have adopted or proposed have been numerous and 
diversified. 

224. The general principle on which compensation pendulums, 
as they are termed, act, may be comprehended from the annexed 
figure and description. 

Suppose C D E F to represent a steel frame, and 
G H a bar of metal connected by the copper rods G 
I and H K with the bar D E , to which they are firm- 
ly fixed. The rod O P being fastened by a pin to 
the bar G H, descends from it through an aperture in 
the bar D E, hanging freely from the point O, and 
supporting the pendulum-bob P : the pendulum turn- 
ing on the suspension-spring A B. Now when the 
longitudinal rods are dilated by heat, the elongation 
of the rods G I and H K, will tend to raise the bar 
G H to which the rod O P is attached ; but the cor- 
responding elongation of the latter will tend to lower 
the point P ; and if the apparatus be properly arrang- 
ed the lengthening of one set of rods will compensate 
that of the other, as they must take place in opposite 
directions. On similar principles are constructed 
Harrison's gridiron pendulum and the numerous sub- 
sequent inventions, the common object of which has 
been to obtain a pendulum-rod, the point of contact 

What character in the pendulum is indispensable in order to make it 
beat seconds ? 

By what circumstances is it prevented from acting in its simple form 
as a perfect regulator ? 

At what season of the year would a clock with a simple pendulum 
move most rapidly ? 





104 MECHANICS. 

or axis of suspension of which shall be at a certain and invariable 
distance from the centre of oscillation. 

225. Thus it has been shown how the effect of a single cause 
of irregularity of action in machinery may be obviated ; but in the 
greater number of the complex machines employed for various 
purposes connected with arts and manufactures, there are often 
several different circumstances contributing more or less to pre- 
vent regular or uniform action. Besides the difficulty of main- 
taining certain points of contact between the moving parts of 
machines, owing to inequality of temperature and consequent con- 
traction and expansion of solid bodies, there are additional diffi- 
culties arising from the gradual wearing away of surfaces by 
friction and from other causes. 

226. But admitting the possibility of preserving the points of 
contact of the parts of a machine invariable for a certain period, 
abundant causes of irregular action might still exist ; among which 
may be mentioned, as one of the most important, the irregular 
effect of the moving power. A familiar example of such a case 
will occur in the common handmill, used by grocers to grind 
coffee or cocoa ; for a greater degree of strength must be exerted 
to turn the winch or handle of such a mill at the lowest point of 
the circle which it forms, in turning, than at the highest point ; 
and thus the machine could not be made to act with an equable 
motion, but for the heavy fly-wheel, connected with the axis of 
the mill, which equalizes the effect, and enables the man to turn 
the mill with any required velocity, working without interruption 
or extraordinary efforts. 

227. The variable inciting forces are, by the intervention of a 
heavy wheel, blended together in creating one great momentum, 
which afterwards maintains a nearly uniform action. The use of 
the fly in mechanics hence resembles that of a reservoir, which 
collects the intermitting currents, and sends forth a regular 
stream.* That distinguished philosopher has given a description 
of a machine called the concentrator of force, by means of which 
an inconsiderable power, acting on a fly-wheel, may be made to 
produce a vast momentary effect. On this principle of the effect 
of the concentration of force depends the action of the coining- 
press used for striking pieces of money. The momentum com- 
municated to the machine by a man whirling round for a few 
seconds the balls at the extremities of a horizontal bar, will cause 

How does the compound pendulum obviate the irregularity of a clock's 
movement? 

What other difficulties besides those already enumerated interfere with 
the action of machines? 

What is one of the most important sources of irregularity in a ma- 
chine? 

What familiar illustration of this irregularity? 

By what means can force be concentrated ? 

How is the coining-press enabled to produce its intense pressure? 

* Leslie's Elements of Natural Philosophy, vol. i. p. 177. 



COMPOUND MACHINERY. 



105 




the screw to descend with such force, carry- 
ing the die against a circular disk of metal, 
as to give it the required impression at one 
stroke. This machine is said to have been 
invented by Nicholas Briot, mint-master 
(tailleur-general des monnoies) to Louis XIII. 
of France ; and by using it one man may do 
as much work as twenty, striking coins with 
a hammer, which was the old method of 
coining.* 

228. A complicated machine, such as the steam-engine, requires 
various modifications or adaptations of its essential parts, and the 
addition of some, peculiar parts to equalize or compensate irregu- 
lar movements, and enable the engine to work with due accuracy 
and effect. Besides the fly-wheel, which is a necessary appen- 
dage to the common low-pressure steam-engine, there is another 
very ingenious and important contrivance, called the governor. It 

consists of two heavy balls, connected by jointed 
rods with a revolving axis, by any increase in 
the velocity of which they diverge or separate 
from each other, and draw downwards the jointed 
rods ; while a slower motion of the axis causes 
the balls to approach each other, and the system 
of rods to be contracted laterally and be extended 
upward. The grand effect produced by this 
means depends on making the ascending and 
descending extremity of the jointed rods raise or 
lower the end of a bar which acts as a lever, and 
moves a valve which regulates the supply of steam from the prin- 
cipal steam-pipe. A similar method of controlling the effect of 
moving power is applicable to wind and water mills, and other 
kinds of machinery. 

229. Whatever may be the complexity of a machine, or however 
varied its action, its effect, theoretically considered, is to be esti- 
mated according to the principles already laid down relative to 
simple machines. There must be in every case an equality of ef- 
fective action in the power and the resistance in order to produce 
equilibrium ; and consequently the efficient force of the power 
must, with the assistance of the machine, exceed that of the weight 
or resistance, before motion can take place. 

230. It may be generally stated that a power can counterbalance 
any given resistance, when the momentum of the former is rendered 
equal to that of the latter. This has been repeatedly demonstral 




In what manner was the process of 
riod of Briot's invention? 



ining performed before the pe- 

On what principle of motion is the mill governor constructed ? 
How is the effect of a compound machine to be estimated ? 
When will motion succeed to a state of rest in any given machine') 

* V. Sigaud de la Fond Elemens de Physique, 1787, t. ii. p. 124. 



106 MECHANICS. 

ed in treating of the several simple machines. Thus, it has been 
shown that a lever can he kept in equilibrium only when the num- 
ber of pounds in the power, multiplied by the number of feet it 
would describe, if put in motion, gives a product exactly equal to 
that of the number of pounds in the resistance multiplied by the 
number of feet in the space relatively described by it ; so that the 
spaces passed through by the power and the resistance must al- 
ways be in the inverse ratio of their respective weights, or actual 
independent forces. Hence it follows that whatever advantage 
is afforded by a machine, so as to enable a small weight or other 
weak power to overcome a great weight or resistance, must de- 
pend on communicating to the power a degree of velocity, or 
causing it to act through a space which shall more than equalize 
the momentums of the antagonist forces. 

231. It may perhaps be remarked that machines, regarded in 
this point of view, give no additional force; since in order to raise 
a weight of 500 pounds, a power must be made to act with an 
effect superior to 500 pounds, either weight or pressure. The 
object of machinery certainly is not to create force, wilich is im- 
possible, but to accumulate, distribute and apply it, so as to pro- 
duce certain effects ; and the advantage thus afforded is often of 
the highest importance. Thus, a man, with a crow-bar, may be 
able to turn over a log of wood, or a block of stone, which unas- 
sisted he could no more move than he could one of the Egyptian 
pyramids. But to raise such a mass of wood, or stone with a 
crow-bar or lever, he must make the end of the bar to which he 
applies his strength move through a space, probably fifty or sixty 
times as great as that through which he would move the log or 
block. So likewise if a man, who could pull with a force only 
equal to 50 pounds, wanted to raise a bale of goods weighing 500 
pounds through the space of 12 feet, he might do it by means of a 
tackle of pulleys, but if it afforded him the assistance precisely 
necessary to supply his deficiency of strength, it must be so con- 
structed that he would have to pull down 120 feet of rope, in order 
to make the bale ascend 12 feet. These examples will probably 
suffice to illustrate the nature of the equilibrium of action resulting 
from the application of machinery; and hence it will be apparent that 
whatever be the moving power employed for any purpose, though 
its actual force cannot be increased by any machine, as such an 
increase would involve physical impossibility, yet its effective force 
may often be indefinitely augmented ; that is, its actual force may 
be made by a machine to overcome an actual resistance, to which, 
alone, it would be utterly inadequate. 

In what proportion to the power and resistance must be the spaces 
which they respectively describe at the commencement of motion ? 

On what must the advantage of a machine for overcoming a great re- 
sistance always depend ? 

What is the true object of machinery in regard to mechanical force? 

How may this be illustrated in the raising of a weight by the aid of a 
lever ? 



THE WEDGE. 107 

232. The action of machinery necessarily requires time to pro- 
duce any given effect. Motion can in no case be instantaneous, 
nowever rapid; and when it is the result of the operation of com- 
plicated machinery, it must be relatively slow. It may indeed 
be the real object of a piece of mechanism to extend a series of 
consecutive movements through a certain period ; and of such an 
arrangement examples may be found in common clocks and 
watches. In an eight-day clock, for instance, a couple of weights 
are wound up to a certain height, and left suspended to act by 
their own gravity in setting in motion trains of wheel-work which 
shall cause the indexes, or hour and minute hands, to describe 
given circles in certain spaces of time, so as to furnish a me- 
thod for the equal measurement of time ; and the gravitating pow- 
ers of the weights are so opposed by the resistance distributed 
over the. numerous wheels and pinions, that though the weights 
may each amount to several pounds, they may descend so slowly 
as to be more than a week in passing through the space of five or 
six feet. 

233. A story is told by an ancient writer, relative to the cele- 
brated Archimedes, from which may be drawn a most pointed 
illustration of the immensity of time and space required to pro- 
duce mechanical effect, where the disproportion between the pow- 
er and the resistance is extremely great. In relating the history 
of the siege of Syracuse by the Romans, Plutarch, in his Life of 
Marcellus, the Roman general, says that Archimedes told Hiero, 
king of Syracuse, whose confidence he possessed, as being re- 
lated to that prince and highly esteemed by him, that by his me- 
chanic skill, he could, if there was another earth for him to stand 
on, move the solid globe which we inhabit. Hiero, astonished at 
this assertion, requested the philosopher to afford him some de- 
monstrative evidence of its truth, by letting him behold a very 
large body moved by a small force ; and the historian adds, this 
effect was exhibited by Archimedes, who sitting on the sea-shore 
drew into port, with one hand, a large ship heavily laden, and 
having a number of men on board. This he is stated to have 
done by gently moving the handle of a machine called polyspas- 
ton, a pulley. 

234. It has been remarked, that if Archimedes had proposed to 
move the earth by means of a lever, and had obtained not only the 
place he required to stand on, but also another whereon to fix his 
fulcrum, with an hypothetical lever of requisite length and strength, 
and had also been endowed with muscular power sufficient to 
enable him to act on the end of his lever so as to move it with the 

With what are the action and effect of machinery necessarily con- 
nected ? 

How are mechanical forces made capable of supplying a measure of 
time.' 

How is the importance of time to mechanical actions exemplified ift 
the celebrated assertion of Archimedes ? 

How did that philosopher illustrate the truth of his statement? 



108 MECHANICS. 

\-elocity of a cannon-ball, he would not have shifted the earth more 
than the twenty-seven millionth of an inch in a million of years ; 
and supposing him to have had but the average power of a strong 
man, it would have taken him 3,653,745,176,803 centuries to have 
moved the earth with the machine he had in view in his address 
to his royal relative.* 

235. Paradoxical as these statements may appear, it may be 
easily shown that they are founded on mathematical evidence. To 
comprehend this it will be only necessary to consider how far into 
boundless space such a theoretical lever as that imagined for Ar- 
chimedes must have extended, and the consequent incomprehensi- 
ble immensity of the arc which such an imaginary lever must be 
supposed to describe. 

236. Those who have leisure and inclination for making such 
computations may ascertain what length of theoretical rope must 
be drawn over imaginary pulleys, to raise through the space of 
one inch, by means of a power equal to seventy-two pounds, a 
spherical mass 8000 miles in diameter, having a mean density 
five times that of water, and taking the weight of a cubic foot of 
that fluid to be 1000 ounces avoirdupois. The result of such a 
calculation would afford an approximation to a fair estimate of the 
fancied task of Archimedes ; and would strikingly evince the utter 
insignificance of human skill and science when contrasted with 
the powers of nature. 



Observations on Friction ,• on the Rigidity of Cordage ,- and on the 
Strength of Materials. 

237. In making calculations or estimates of the effective force 
of moving powers applied to machinery, it is always necessary to 
admit certain deductions on account of the obstacles to freedom 
of motion arising from friction, the rigidity of cordage, or the im- 
perfections of the materials of which machines must be construct- 
ed. All these subjects are of the highest importance to practical 
mechanicians, and are therefore deserving of the most accurate 
attention ; but it will be sufficient here to describe briefly the 
nature of these obstructing or retarding forces, and to notice the 
methods usually adopted for lessening or correcting the inconve- 
niences they may produce. 

How rapidly might the theoretical lever of Archimedes have enabled 
him to move the earth ? 

What are the elements of calculation to show the practical result of 
such an attempt } 

In what light would the computation place human skill and artificial 
powers ? 

On what accounts are deductions from the theoretical effects of ma- 
chines rendered necessary ? 

* Recreations in Mathematics and Natural Philosophy, edited by Dr. 
Charles Hutton, vol. ii. p. 19. 



FRICTION. 109 

238. It is the well-known consequence of friction that when 
one substance moves in contact with another, either at rest or 
moving in an opposite direction, more or less force must be applied 
to produce motion in proportion to the roughness or smoothness 
of the surfaces of the tw r o bodies. No substance can be perfectly 
smooth: not even polished steel or glass. Those surfaces that to the 
naked eye seem free from the slightest inequalities are found, 
w r hen examined by a powerful microscope, to be covered with in- 
numerable rising points and hollows, like the face of a file ; and 
sometimes to be intersected by abundance of irregular ridges and 
furrows. Now when surfaces, such as nave been just described, 
are made to move in contact, the prominent parts of the one will 
pass into the depressions of the other, and thus occasion more or 
less difficulty in procuring lateral motion. 

239. Though friction, from its effect in retarding motion, lessens 
the advantage derived from machinery, and often causes inconve- 
nience, yet it is one of those properties of matter which we find tc 
be of almost indispensable utility. If all bodies were destitute of 
friction it would be very difficult for us to grasp or retain in our 
hands any solid substance ; a penknife, a ruler, or a book would 
slip through our fingers, if not held tightly ; and in using our 
hands for any purpose, such a degree of muscular power must be 
exerted as would be extremely fatiguing and inconvenient. But 
without friction it would be still more difficult to use our feet than 
our hands ; and no man could walk upright unless he possessed 
the skill and activity of a tight-rope dancer, or a performer on the 
slack- wire. 

240. The consequence of losing the advantage derived from 
friction in walking, may be easily conceived, when we reflect on 
what takes place when friction is partially destroyed by the streets 
and open pavements being covered with ice, as occasionally hap- 
pens during the winter season. Arming the soles of the shoes 
with list, or with projecting nails, and covering the ice with saw- 
dust, ashes, or other loose substances, are among the usual methods 
resorted to at such times, to restore friction, and enable people to 
w^alk steadily. 

241. Friction is likewise advantageously used as a means of 
sharpening or polishing various substances, by rubbing, grinding, 
and other operations of great importance in several arts and manu- 
factures. This property of matter may even be applied to the 
production of motion ; at least it may be made the medium of com- 
munication between one part of a machine and another. Thus 

To what is the resistance from friction always proportioned ? 
What is the true nature of surfaces commonly considered smooth? 
Ry what means is the true character of surfaces to he detected ? 
What is supposed to be the real mode of action by which friction op- 
poses, retards, or destroys motion ? 

Of what advantage is friction in the ordinary purposes of life ? 
How is its importance in walking made apparent ? 
How is friction employed in manufacturing processes ? 
K 



110 MECHANICS. 

wheels are sometimes covered on their peripheries with buff-lea- 
ther, and one of them being set in motion will then turn the other, 
by the friction of the rough surfaces of the leather, acting as if the 
wheels had been furnished with innumerable series of minute 
teeth. 

242. Such are the benefits of friction, but in many cases it 
proves a very inconvenient property of matter, hindering freedom 
of motion, and tending to obstruct it entirely ; and hence in the 
construction of machinery various contrivances are adopted to 
lessen or destroy the effect of friction. Systematic writers have 
distinguished this property of matter into two kinds : namely, 
1. That which takes place when two flat surfaces are moved in 
contact, so that the same points of one surface are constantly ap- 
plied to some part of the other ; and 2. The friction that takes 
place when one body rolls over another, so that the points of con- 
tact of both surfaces are perpetually changing. The former may 
be styled dragging friction, and the latter rolling friction.* It 
must be obvious that the retarding effect of the former must be 
vastly greater than that of the latter kind of friction. It is for this 
reason that plumbers, masons, and' carpenters, when they want to 
move a heavy mass of metal, stone, or wood, place beneath it 
several cylinders of hard wood, by means of which such a mass 
may be dragged forward without coming in contact with the 
ground , and the immense friction of the first kind or dragging fric- 
tion which must otherwise occur, is changed into rolling friction 
or rolling motion. On the other hand rolling friction is converted 
into dragging friction, by shoeing or locking the wheel of a car- 
riage in going down a steep hill. 

243. On the principle just stated depends the utility of those 
parts of some complex machines, called friction-wheels. In 
wheel-work the chief friction takes place between a wheel and the 
axle on which it turns ; and to diminish its effect it is usual to 

How may it serve as a means of communicating motion ? 

Into how many kinds has friction been divided by systematic writers ? 

Which of these exists in the mechanical devices for moving heavy 
masses ? 

What kind of friction exists at the axle, and what at the periphery of 
a carriage-wheel ? 

How is the friction of the axis of carriage-wheels diminished by means 
of rollers ? 



* The terms rolling and dragging friction seem more appropriate than 
interrupted and continued friction ; as expressive of the mode of action 
by which they are respectively produced. A true case of rolling friction 
takes place only when the rollers are so situated as to have no necessity 
of employing axles ; as when cylinnders or cannon-balls are placed be- 
neath heavy weights. The wheel-carriage is not a case of this kind, for 
it only transfers the friction which would take place at the periphery if 
the wheel were locked to the axle, which experiences a dragging friction 
within the box. — See on this subject Journal of the Franklin Institute, 
vol. 5, p. 57. — Ed. 




RIGIDITY OF CORDAGE. Ill 

construct the axle and the box, or central part of the wheel, of 
very hard substances, the surfaces of which are not only rendered 
as smooth as possible, but also covered with oil, or some other 
unctuous matter, which facilitates the motion of the corresponding 
parts. But where it is necessary to obtain the utmost facility of 
motion, a method has been adopted for subdi- 
viding friction, by letting the axle of a princi- 
pal wheel move on two or more small wheels, 
as in the marginal figure. These are named 
friction-wheels. * 

244. In estimating the effect of friction, so 
many circumstances must be taken into the 
account, that the result, in any given case, may 
afford but little assistance in deciding others. It may however 
be stated, as the most important deduction from repeated experi- 
ments, that friction does not depend on the extent of the surfaces 
on which it acts, but chiefly on the degree of pressure to which 
they are subjected ; so that, the surfaces continuing in the same 
state, increase of pressure will produce increase of friction. 

245. When a heavy body is placed on an inclined plane, it will 
have a tendency to slide ; and consequently will remain at rest on 
such a plane, only when the retarding effect of friction is greater 
than the tendency for motion, caused by the inclination of the 
plane. Hence the angle of inclination at which motion on an in- 
clined plane commences, has been styled the angle of friction ; 
and it will of course be different in different cases, according to 
the nature of the rubbing surfaces, and the degree of pressure. 

246. The rigidity of cordage is another property of solid bodies 
which interferes with the freedom of motion in some kinds of ma- 
chinery. It must necessarily depend on the peculiar nature of 
the materials used, since the more flexible they are, the more rea- 
dily will they become adapted to the wheels or spindles around 
which they are coiled ; and the smaller will be the interruption 
of regular continued motion. It is principally when very thick 
lines are used, such as the cables for heaving anchors for very 
large ships, that this rigidit)'' of cordage becomes a serious impe- 
diment to motion, requiring the expenditure of great force to over- 
come it. Iron chains have been advantageously introduced into 
the maritime service, instead, of cables ; and are likewise employ- 

What is one of the most important deductions from experiments on 
friction ? 

What is meant by the angle of friction? 

Is this angle constant or variable ? 

To what does the rigidity of cordage usually offer its resistance ? 

What substitutes for large cahles have of late been adopted ? 

* The railroad cars of Winans, Howard, and several others, employing 
friction-wheels, have beerv invented in the United States, and will be 
found described in the early volumes of the Journal of the Franklin In- 
stitute. — En. 



1 1 2 MECHANICS. 

ed for various purposes in the arts to which ropes alone were for- 
merly considered applicable. 

247. In the construction of machines much must depend on the 
strength and firmness of the materials of which they may be com- 
posed. Thus, in the case of one of the most simple machines, 
the lever, suppose a long pole to be applied to raise a considera- 
ble weight, much of the effect of any power would be lost in con- 
sequence of the bending of such a wooden lever at that part which 
rested on the fulcrum ; and therefore an iron bar, nearly inflexible, 
of the same length with the pole, would enable a man to move any 
given weight or resistance with less exertion. 

248. The hardness, tenacity, elasticity, and other properties of 
bodies, on which their relative strength must principally depend, 
vary so greatly even in different specimens of the same substance, 
as wood or metal, that few rules of general application can be 
given for computing the degrees of force, which may be applied 
with safety to the particular parts of any complex machine. Any 
solid substance, as a bar or rod of iron, may be subjected to ten- 
sion or pressure in different ways : as, (1), by suspending to it a 
great weight, or endeavouring to stretch it longitudinally ; (2), 
by weight or pressure applied to crush or compress it; and (3), 
by weight or pressure applied to the centre of a bar or rod its 
extremities alone being supported. 

249. It appears from experiment, that in the first case, the 
length of a rod remaining the same, its strength will be increased 
or diminished in proportion to the area of its transverse section ; 
thus, as 27 tons weight will tear asunder an iron bar one inch 
square, so a bar but half a square inch in the section will be 
broken by a weight of 13^ tons ; and so on in any given propor- 
tion. Concerning the capacity of bodies for resisting compres- 
sion, but little is known with certainty. Much appears to depend 
on the form of a body, for a cubic inch of English oak required to 
crush it a weight of 3860 pounds ; but a bar an inch square and 
five inches high gave way under the weight of 2572 pounds ; and 
if longer it would manifestly have broken with a less weight. 
Mr. Rennie, one of the architects of London Bridge infers from 
calculation that the granite of which the great arch of that bridge 
is constructed would bear a pressure equal to four tons upon every 
square inch of its upper surface. 

250. As to the strength of bodies exposed to transverse or late- 
ral pressure, one or both ends being supported, it depends on the 
dimensions of a section of the body in the direction of the pres- 

On what circumstances must the usefulness of machines chiefly depend ? 

Name some of the physical properties of materials which vary their 
usefulness in the mechanic arts. 

In how many ways may a solid rod of any material be subjected to me- 
chanical action ? 

Hnw is direct tension applied? how crushing pressure? how cross 
strain ? 

What inference has been drawn by Rennie from experiments on gra- 
aite ? 



MOVING POWERS. 113 

sure. Thus a beam having' the same length and breadth with 
another, but twice its depth, will be four times as strong ; and a 
beam double the length of another, but with the same breadth 
and depth, will have but half as much strength. Hence the 
strength of solid bodies is not by any means to be estimated by 
their absolute magnitude. 

251. Hollow cylinders are much stronger than solid ones of 
equal length and weight ; and therefore it appears an admirable 
provision of nature that the bones of men and other animals in 
those parts requiring facility and power of motion are more or less 
of a cylindrical shape, with cavities in the centre, which in birds 
are filled only with air, whence partly their capacity for flight ; 
but in men and beasts the cavities are filled with alight oily fluid, 
which congeals after death, forming marrow. The strength or 
efficient power of an animal depends chiefly on the accurate con- 
struction and adaptation of its several parts. 

'252. Some very small creatures possess muscular power, in 
proportion to their bulk, incomparably greater than that of the 
largest and strongest of the brute creation. A flea, considered 
relatively to its size, is far stronger than an elephant or a lion ; as 
will appear from comparing the distance the insect would leap at 
one bound with its actual dimensions, with reference to the spring 
and dimensions of the quadruped. Some marine animals, as the 
whale, are of vast bulk ; nature having provided for their conve- 
nience by giving them a medium of great density to inhabit. 

Moving Powers. 

253. The original forces which produce motion, and which have 
been denominated Moving Powers, or Mechanical Agents, are of 
various kinds, depending on the natural properties of bodies. Gra- 
vitation or weight is an extensively acting power affecting matter 
in all its different forms, and affording the means of originating 
motion for many useful and important purposes. By the proper 
application of weight is excited and maintained the equable motion 
of wheel-work, as in a common clock ; and the same power differ- 
ently adapted is made to act by percussion, in pile-driving and 
numerous other operations. Currents of water owe their velocity 
to the weight of the descending liquid, yielding a kind of moving 
power on which depends the effective force of water-wheels and 
other hydraulic engines. 

254. Elasticity is another property of matter which gives ener- 

What relation exists between the dimensions of a beam and the resist- 
ance which it is capable of opposing to cross strain ? 

What advantage does the hollowness in the bones afford to the strength 
of animals ? 

How are we to judge of the relative strength of insects and of large 
animals ? 

What is one of the most common mechanical forces, and in what dif- 
ferent modes is its efficacy applied ? 

K 2 



114 MECHANICS. 

gy to various mechanical agents. -Elastic metals, as steel, manu- 
factured into springs, are used in the construction of watches or 
chronometers ; and the contractile force of springs is employed for 
many other purposes, as in roasting-jacks and weighing-machines. 
Liquids, though compressed with difficulty, display a high degree 
of poAver when thus treated ; and machines of vast energy have 
been invented, the effect of which depends on the expansive or 
elastic force of compressed water. The elasticity of air is like- 
wise an abundant source of moving power. Steam-engines, such 
as were used in the early part of the last century, were made to 
act through atmospheric pressure, arising from the joint influence 
of the weight and elasticity of the air ; but since the vast improve- 
ments in machines of this description, in consequence of the re- 
searches of Watt, and other experimental philosophers, steam or 
elastic vapour is employed as the sole moving power, and so 
managed as to produce effects far beyond those of the old atmo- 
spheric engines. 

255. Heat must be regarded as a moving power, the efficacy 
of which depends on its tendency to dilate different kinds of mat- 
ter. It also converts solid bodies to the liquid state, and liquids 
under its influence are changed into vapours or gases. Hence 
indeed is to be explained the operation of the steam-engine, in 
which alternating motion is produced by the expansive force of 
steam or water raised to the state of vapour by means of heat. 
Combustion is a chemical process, often excited by heat, and 
during the progress of which heat is always developed ; and from 
this source is derived moving power of vast intensity, as occurs 
in the discharge of shot or balls from fire-arms, through the ex- 
plosion of gunpowder. In this case the moving power arises from 
the sudden expansion of gases formed by the combustion of solid 
matter ; but engines have recently been constructed the action of 
which depends on the formation of a partial vacuum by the in- 
flammation of oxygen and hydrogen gases in close vessels, and 
the consequent production of water. 

256. Machines may be set in motion by means of electricity, 
galvanism, or magnetism ; and forces, which have been chiefly 
regarded as objects of curiosity may be extensively applied to 
useful and important purposes. In a French periodical publica- 
tion (Journal de Geneve, 1831), some account is given of an elec- 
trical clock, invented by M. Bianchi of Verona. This timekeeper 
has neither weight nor spring, instead of which the constant vibia- 

State some of the amplications of elasticity to purposes connected with 
the arts ? 

What is the difference in principle between the atmospheric engine of 
Newcomen and the modern steam-engines of Watt and Evans ? 
On what is the efficacy of heat as a moving power dependent ? 
In what other modes is heat occasionally applied to produce mechanic 
ction ? 

What other imponderable agent, besides heat, is occasionally employ- 
dasa moving force ? 



HUMAN STRENGTH. 115 

tion of the pendulum is maintained by the impulse of electricity, 
which it receives by moving- between two galvanic piles, the ball or 
or bob being 1 furnished with a conductor, which in its oscillations, 
approaching either pile, alternately, is repelled by the discharg-e 
of the electric fluid; and the regular action of the whole of the 
machinery is kept up. 

257. These cursory observations will afford some general ideas 
of the nature and extent of the moving - powers originating- from 
the influence of elastic fluids, heat, and electricity ; but the further 
discussion of these topics must be referred to the subsequent por- 
tion of this work, where the phenomena connected with these 
subjects will be distinctly noticed. There are, however, besides 
those moving powers, the operation of which' depends on the phy- 
sical properties of matter in different states of aggregation, other 
mechanical agents, the effects of which arise from the vital ener- 
gy of animated beings ; and concerning these some details may 
here be properly introduced. 

258. The application of the natural strength of man must have 
preceded the employment of all other moving- powers ; and we 
know from history, that ever since a very remote period brute ani- 
mals have likewise been rendered subservient to the purposes of 
art and industry. The employment of oxen and horses in the 
labours of the field must have originated in the earliest ages ; and 
the art of training beasts of different kinds to exert their strength 
for the benefit of man has been known and practised among almost 
all nations except those in the very rudest state of society. 

259. The mechanical effects produced by the muscular exertions 
of living beings cannot be subjected to calculation on precisely 
the same principles as the moving power of a weighing-machine 
or a steam-engine ; nor even can they be estimated with so much 
precision as the efficient power of a windmill or a water-wheel ; 
but there are modes of obtaining data whence to determine the 
value of animal strength as a mechanical agent, which may serve 
to indicate the comparative product of labour from that and other 
sources, and enable us to discover their relative importance for 
any given purpose. 

260. The usual method of computing the mechanical value or 
efficiency of labour is from the weight it is capable of elevating to 
a certain height in a given time, the product of these three mea- 
sures (weight, space, and time) denoting the absolute quantity of 
performance. But these measures have obviously a mutual rela- 
tion which will affect the result ; for great speed will occasion a 

Describe Bianchi's galvanic clock. 

On what do the effects of animal efforts depend when employed for 
mechanical purposes ? 

What were among the earliest zootic moving forces employed in the 
arts ? 

Can the power of animals be accurately computed by their weight and 
velocity ? 

What three elements enter into the computation of animal power ? 



116 MECHANICS. 

Waste of force, and shorten the period during- which it can be ex- 
erted. It was computed by Daniel Bernoulli and Desaguliers 
that a man could raise two millions of pounds avoirdupois one 
foot in a day. But some writers have calculated that a labourer 
will lift ten pounds to a height of ten feet every second, and 
continue to work at that rate during ten hours in a da3', raising in 
that time 3,600,000 lbs. But these estimates are certainly incor- 
rect, and appear to have been founded on inferences drawn from 
momentary exertions under favourable circumstances. Smeaton 
states that six good labourers would raise 21,141 cubic feet of 
sea-water to the height of four feet in four hours ; so that they 
would raise about 540,000 pounds each to the height of ten feet 
in twenty-four hours. 

261. Coulomb has furnished some of the most exact and varied 
observations on the measure of human labour. A man will climb 
a staircase from 70 to 100 feet high, at the rate of 45 feet in a mi- 
nute; and hence, reckoning the man's weight at 155 pounds, the 
animal exertion for one minute would be 6075, and would amount 
to 4,185,900, if continued for ten hours. But such exercise would 
be too violent to be thus continued. A person might ascend a 
rock 500 feet high by a ladder-stair in twenty minutes, or at the 
rate of 25 feet a minute : his efforts are thus already impaired, 
and the performance reduced to only 3875 in a minute. 

262. But with the incumbrance of a load the quantity of action 
must be yet more remarkably diminished. A porter weighing 
140 pounds, who could climb a staircase forty feet high two 
hundred and sixty-six times in a day, was able to carry up only 
sixty-six loads of fire-wood, each weighing 163 pounds. In the 
former case, his daily performance was very nearly 1,489,600; 
while in the latter it amounted to only 799,920. The quantity 
of permanent effect in the latter case* therefore was only about 
800,000, or little more than half the labour exerted in mere climbing. 
A man, drawing water from a well by means of a double bucket, 
may raise 36 pounds one hundred and twenty times a day, from a 
depth of 120 feet, the total effect being 518,400. A skilful labourer 
working in the field with a large hoe produced an effect equal to 
728,000. When the agency of a winch is employed in turning a 
machine, the performance is still greater, amounting to 845,000. 

263. The effective force of human exertion differs according to 
the manner in which it is applied. From some experiments mad^ 
by Mr. Robertson Buchanan, it was ascertained that the labour 
of a man employed in working a pump, turning a winch, ringing 

What are the suppositions adopted by Bernoulli and Desaguliers in re- 
gard to the amount of human effort ? 

To what results did Coulomb arrive in respect to the speed of human 
movements, and to the continued daily labour of men when working only 
to raise their own weight, and when carrying up additional burdens ? 

According to what circumstances does the effective force of human ex- 
ertion vary ? 

* The useful effect in the former case was 0; in the latter it was 430,320. 



HUMAN STRENGTH. 117 

a bell, and rowing a boat, might be represented respectively by the 
numbers 100, 167, 227, and 248. Hence it appears that the act of 
rowing is an advantageous method of applying human strength. 

264. A London porter is. accustomed to carry a burden of two 
hundred pounds at the rate of three miles an hour ; and a couple 
of Irish chairmen will walk four miles an hour, with a load of 300 
pounds. But these exertions are by no means equivalent to those 
of the sinewy porters in Turkey, the Levant, and other parts bor- 
dering on the Mediterranean. At Constantinople, an Albanian 
will carry 800 or 900 pounds on his back, stooping forward, and 
assisting his steps by a short staff. At Marseilles, four porters 
commonly carry the immense load of nearly two tons, by means of 
soft hods passing over their heads, and resting on their shoulders, 
with the ends of the poles from which the goods are suspended. 

265. The most extraordinary instances of muscular exertion in 
the carriage of burdens are those exhibited by the cargueros or 
carriers, a class of men in the mountainous parts of Peru, who 
are employed in carrying travellers. Humboldt, in relating the 
circumstances of his descent on the western side of the Cordillera 
of the Andes, gives some account of the cargueros. It is as usual 
in that country for people to talk of going a journey on a man's 
back, as it is in other countries to speak of going on horse back. 
No humiliating idea is attached to the occupation of a man-carrier , 
and those who engage in it are not Indians, but Mulattoes, and 
sometimes whites. The usual load of a carguero is from 160 to 
180 pounds weight, and those who are very strong will carry as 
much as 210 pounds. Notwithstanding the enormous fatigue to 
which these men are exposed, carrying such loads for eight or 
nine hours a day, over a mountainous country, though their backs 
are often as raw as those of beasts of burden, though travellers 
have sometimes the cruelty to leave them in the forests when they 
fall sick, and though their scanty earnings during a journey of 
fifteen or even thirty days is not more than from 11 to 12 dollars, 
yet the employment of a carguero is eagerly embraced by all the 
robust young men who live at the foot of the mountains.* 

266. The different races of mankind display much diversity of 
muscular strength ; though in all cases much must depend on the 
constitution and habits of the individual. M. Peron f has stated 
the results of some interesting experiments which he made to 

In what kind of exertion did Buchanan find the greatest, and in what 
the least advantageous employment of the strength of men ? 

What striking examples can you enumerate of the transportation of 
heavy loads ? 

Who are the cargueros, and what feats of strength are related of them 
by Humboldt? 

* See Humboldt's Researches concerning the ancient inhabitants of 
America; with Descriptions of the most striking Scenes in the Cordille- 
ras. London, 1814. 

t Voyage de Decouvertes aux Tcrres Australes, fait par ordre du gou 
vernment pendant les annees 1800 — 4. 



118 MECHANICS. 

discover the relative mechanical power of individuals of different 
nations. For that purpose he used an instrument called a Dyna- 
mometer, which, by the application of spiral springs, to a gradu- 
ated scale, afforded the means of estimating the forces exerted by 
the persons who were the subjects of his experiments. He col- 
lected by this method a number of facts, which he conceived suf- 
ficient to enable him to deduce from them the medium forces or 
powers of exertion of the inhabitants of the Island of Timor, of 
New Holland, and Van Diemen's Land, and to compare them 
with those of the English and the French. The following is the 
order of arrangement, commencing with the weakest: Manual 
fn rce — Van Diemen's Land, N. Holland, Timor, French, English. 
The proportion between the two extremes is nearly as 5 to 7. 
Lumbo-dorsal force, [force des reins'] — the order the same as 
before; but the proportion between the extremes, as 5 to 8. 

267. The labour of a horse in a day is usually reckoned equal 
to that of five men; but then the horse works only eight hours, while 
a man can easily continue his exertions for ten. Horses display 
greater power in carrying than in drawing ; yet an active walker 
will beat them in a long journey. Their effective force in traction 
seldom exceeds 144 pounds, but they are able to carry six times 
that weight.* The pack-horses in the West Riding of Yorkshire, 
England, are accustomed to convey loads of 420 pounds over a 
hilly countr} r ; and in many parts of that country the mill-horses will 
carry the burden of even 910 pounds, for a short distance. 

268. The most advantageous load for a horse must be that with 
which his speed will be greatest in proportion to the weight car- 
ried. Thus, if the greatest speed at which a horse can travel 
unloaded be 15 miles an hour, and the greatest weight he could 
sustain without moving be supposed to be divided into 225 parts, 
then his labour will be most effective when, loaded with 100 of 
those parts, he travels at the rate of five miles an hour. The com- 
mon estimate of horse-power adopted in calculating the effect of 
steam-engines is wholly hypothetical. It is stated by Watt to be 
that which will raise a weight of 33,000 pounds the height of one 
foot in a minute of time, equal to raising about 90 pounds four 
miles an hour. Another estimate reduces the weight to 22,000 
pounds raised one foot in a minute, equivalent to 100 pounds 2J 
miles an hour. This mode of calculation seems to have been intro- 
daced as a matter of convenience, when the use of horses in mills 
and factories was superseded by that of steam-engines ; and must 
have been adopted in order to show the superiority of steam- 
To what extent did Peron discover that different nations vary in the 

forces which they can exert in different modes of exertion ? 

In what manner do horses exert their strength to greatest advantage ? 

What is generally found to be their effective force of traction ? 

What will he found the most advantageous load for a horse ? 

What is the estimate of horse-power assigned by Watt in calculating 
the effect of steam-engines ? 

* It does not follow that it is better to use pack-horses than wagons. — Ed. 



ANIMAL STRENGTH. 119 

engines over horses according to the most exaggerated statement 
of the power of the latter. 

269. The ass, though far inferior to the horse in strength, is yet 
a most serviceable beast of burden to the poor, as lie is easily 
maintained at little cost. It has been found that in England, an 
ass will carry about 220 pounds twenty miles a day ; but in 
warmer climates, where he becomes a larger and finer animal 
he may be made to trot or amble briskly with a load of 150 
pounds. 

270. Dogs are now frequently used for draught in various conn- 
tries. The Kamtschatdales, Esquimaux, and some other north- 
ern people, employ teams of dogs to draw sledges over the frozen 
surface of snow. They are harnessed in a line, sometimes to the 
number of eight or ten, and they perform their work with speed, 
steadiness, and perseverance. Captain Lyon, when he visited the 
Arctic regions, had nine of these dogs, who dragged 1610 pounds 
a mile in nine minutes, and worked in this manner during seven 
or eight hours in a day. Such dogs will draw a heavy sledge to 
a considerable distance, at the rate of 13 or 14 miles an hour; and 
they will travel long journeys at half that rate, each of them pul- 
ling the weight of 130 pounds. * 

271. The elephant was used by the Romans for the purposes 
of war, as it is still in India, and other oriental counties. His 
strength is reckoned equivalent to that of six horses, but the quan- 
tity of food he consumes is much greater in proportion. An ele- 
phant will carry a load of 3000 or 4000 pounds ; his ordinary pace 
is equal to that of a slow-trotting horse ; he travels easily 40 or 
50 miles a day; and has been known to go 110 miles in that 
time. 

272. The camel is a most valuable beast of burden on the sandy 
plains on both sides of the Red Sea; for traversing which, the 
animal might seem to have been expressly created. Some camels 
are able to carry 10 or 12 hundredweight; others not more than 6 
or 7 ; and with such loads they will walk at the rate of 2 J miles 
an hour, ancl travel regularly about 30 miles a day, for many days 
together, being able to subsist eight or nine days without water, 
and with a very scanty supply of the coarsest provender. 

273. The dromedary is a smaller species of camel, chiefly used 
for riding, being capable of travelling with greater speed than the 
larger camel, but not equally proof against exhaustion. The best 
Arabian camel or dromedary, after three whole days' abstinence 

For what purposes have dogs often been employed? 
At what speed, and with what loads, can the Arctic dogs travel ? 
At what speed, and with what load, can the elephant travel? 
What circumstances of its constitution adapt the camel for usefulness 
in the particular climate where it is found to subsist? 
For what particular labour is the dromedary adapted ? 

* The exhibition called the Hall of Industry, shows the force of dogs 
applying their strength on & flexible inclined plane. — E». 



\ 

120 MECHANICS. 

from water, shows manifest symptoms of great distress; though 
it might possibly be able to travel five days without drinking - ; 
which, however, can seldom or never be required, as it appears 
that, in the different routes across the desert of Arabia, there are 
wells not more at the utmost than 3<j days' journey from each 
other. Exaggerated statements have been given of the speed of 
this animal ; the most extraordinary performance of which the 
traveller Burkhardt ever obtained authentic information having 
been a journey of 115 miles in eleven hours, including two passa- 
ges across the Nile in a ferry-boat, requiring twenty minutes each. 
The same traveller conjectured that the animal might have travel- 
led 200 miles in twenty-four hours. A Bedouin Arab has been 
known to ride express from Cairo to Mecca, 750 miles, upon a 
dromedary, in five days. Twelve miles an hour is the utmost 
trotting-pace of the smaller carnel ; and though it may gallop 9 
miles in half an hour, it cannot continue for a longer time that 
unnatural pace. It ambles easily at the rate of 5§ miles an hour; 
and if fed properly every evening, or even once in two da) r s, it will 
continue to travel at that rate five or six days. 

274. The lama, or guanaco, is a kind of dwarf camel, which 
is a native of Peru ; and it was the only beast of burden employed 
by the ancient inhabitants of that country. It is easily tamed, 
feeds on moss, and being admirably adapted for traversing its usual 
haunts, the lofty Andes, it is still employed to carry goods. The, 
strongest of these animals will travel, with a load of from 150 to 
200 pounds, about fifteen miles a day over the roughest moun- 
tains. There is a smaller animal of a similar nature, called the 
Pacos, which is also now used by the Peruvians in transporting 
merchandise over the mountains ; but which will carry only from 
50 to 70 pounds. 

275. Oxen have been, in many countries, employed in the la- 
bours of husbandry, instead of horses. They are, however, infe- 
rior, not only on account of the softness of their hoofs, which 
renders them, if unshod, unfit for any except field work, but 
likewise as being comparatively unprofitable. A team of oxen 
capable of ploughing as much land as a pair of horses will require 
for support the produce of one-fourth more land, after allowing for 
the increase of weight and value. 

276. In some parts of Europe the goat is made to labour, by 
treading a wheel to raise ore or water from a mine. They are, in 
England, sometimes harnessed to miniature carriages for children ; 
and in Holland the children of the rich burghers are thus drawn 
D y goats, gaily caparisoned, and yoked to light chariots. The 

What is the greatest speed of the camel ? 
At what constant rate can it usually travel ? 
What is the load and speed of the lama of South America ? 
Why are oxen inferior to horses in the lahours of husbandry r 
In what manner lias the goat been employed as a mechanical agent ? 
In what region, and for what purpose, is the rein-deer made subser- 
vient to the purposes of man ? 



ANIMAL STRENGTH. 121 

rein-deer of Lapland is a most serviceable beast of draught in the 
frozen regions of the north. Two of these deer, harnessed to a 
sledge for one person, will run 50 or 60 miles on the stretch ; and 
they have been known to travel thus 112 miles in the course of a 
day. 

At what speed can this animal travel ? 



The foregoing statements and illustrations will, in general, be 
found sufficient for the class of students for whose use this work 
is chiefly designed. For the use of teachers and others who may 
desire to pursue the subject more into detail, and to find rigorous 
demonstrations of the principles above laid down, we would make 
the following references to works which may with more or less 
facility be obtained by the American reader. 

Cambridge Mechanics, by Prof. Farrar, p. 13 — 278. 
Fischer's Elements of Natural Philosophy, p. 10 — 52. 
Playfair's Outlines of Natural Philosophy, p. 19 — 168. 
Boucharlat, translated from the French by Professor Courtney 
Gregory's Mechanics. 

Library of Useful Knowledge, article Mechanics, three num- 
bers. 
Robinson's Mechanics, edited by Dr. Brewster, in 4 vols. 
Young's Mechanics. 
Lagrange Mecanique Analytique. 
Biot Traite de Physique. 
Journal of the Franklin Institute, passim. 

Many more works might be named, but the above it is believed 
will constitute a sufficient collection of subsidiary works to aid 
the teacher in his private investigations under the different heads 
embraced in the preceding treatise. — Ed. 



HYDROSTATICS. 

1. As the science of Mechanics treats of the phenomena depend- 
ing on the properties of weight and mobility in solid bodies, so 
Hydrostatics relates to the peculiar effects of the weight and mo- 
bility of liquids. The term hydrostatics properly denotes the 
stability of water,* or in a more extensive acceptation, the pres- 
sure and equilibrium of liquids at rest. The effects produced by 
the flowing of water or any other liquid, have sometimes been 
regarded as appertaining to a distinct department of natural phi- 
losophy, named Hydraulics ;j- and occasionally the whole doctrine 
of mechanical science as applicable to liquids has been treated 
of under the designation of Hydrodynamics,^: which, however, 
seems to possess no such peculiar property as to warrant its gene- 
ral adoption ; and therefore the term Hydrostatics may be retained 
as denoting the science whose object is to explain the phenomena 
arising from the influence of gravitation on water and other 
liquids whether in the state of rest or in that of motion. 

2. Liquids differ in some of their distinguishing properties from 
solids, and in others from gases or aerial fluids ; forming an inter- 
mediate class of bodies. A solid, by the disintegration of its parts, 
may be reduced to a state bearing some resemblance to that of a 
liquid, thus fine sand or any light powder will yield to pressure in 
every direction, almost as readily as water; but the resemblance 
is still extremely imperfect. Viscous fluids, as train oil or trea- 
cle, approach to the nature of solids ; and indeed the distinction 
between such liquid substances and some of the softer solids, as 
butter or honey, depends much on their relation to heat, their con- 
sistence or relative density varying with the temperature to which 
they are exposed. 

3. As the effect of temperature on different bodies will consti- 
tute the subject of a separate treatise, it will be sufficient at pre- 
sent to state that, the peculiar degrees of density and tenacity of 
unorganized substances, constituting the respective states of soli- 
dity and fluidity, with their various modifications, seem to be 
chiefly influenced by heat and pressure ; so that a particular sub- 
stance, as water, may exist under different forms, depending on 
the circumstances in which it is placed. Thus a certain degree 
of cold will convert water into a hard solid, as ice or hail, which, 
when melted by heat, produces a liquid differing in no respeci 
from the water of which it was formed ; and this when exposed 

To what is the term hydrostatics properly applied ? 

To what is hydraulics sometimes appropriated ? 

What other term has heen used to denote the mechanical properties 
and effects of liquids ? 

In what manner may solid substances be made to resemble liquids? 

What class bfliquids bear an analogy to solid bodies P What circum- 
stances influence the density and tenacity of unorganized substances } 

i * From T^wp, water, and a-raa-ts, standing. f From icSmp, and «u\o ? , a 
pipe. t From raw, and Juv^jc, power. 

122 



OF LIQUIDS. 123 

to a sufficiently high temperature, will evaporate or become steam, 
which may be again condensed or restored to the liquid state by 
cold. Mercury commonly occurs in the form of a very dense 
liquid ; but it may, like water, be condensed or frozen by exposure 
to an extremely low temperature, and be made to boil or evapo- 
rate by subjecting- it to a great degree of heat. The other metals 
differ from mercury only in remaining solid in higher temperatures 
than that substance ; but they all melt with various degrees of 
heat, and become sublimed or evaporated when the heat is greatly 
raised above the melting point. 

4. Since the same kind of matter may exist under different 
states or forms, it follows that liquids must be composed of the 
same particles as solids, and the difference between a liquid and 
a solid may be conceived to arise, merely, from peculiar modifica- 
tions of the cohesive attraction which takes place between the 
constituent molecules or particles of such bodies respectively. 
The particles of elastic solids must be capable of a sort of vibra- 
tory motion, from sudden pressure, but they will always resume 
the same position as soon as the vibration ceases, unless it be so 
violent as to occasion a permanent separation of the particles, 
when the solid becomes broken or pulverised. Now liquids have 
their constituent particles, held together like those of solids, by 
cohesive attraction, but they oscillate on the application of the 
slightest impulse ; and there seems to be such a general relation 
of all the particles to each other, that when the connexion between 
any two particles is broken, by shaking or otherwise agitating 
the mass of which they form a portion, they readily become at- 
tracted by any other particles with which they may happen to 
come in contact, new cohesions take place, and when the dis- 
turbing force is removed, the general equilibrium is restored 
throughout the liquid mass. 

5. The cohesive attraction between the particles of liquids is 
demonstrated by the globular figure which they assume, when no 
external force interferes with the aggregation of the mass. This 
appears in the case of mercury thrown in small portions on a china 
plate, or on any surface which exercises on it no chemical attrac- 
tion ; when the minute portions into which it will become separated, 
will be found to be perfect spherules, the larger ones only being 
slightly flattened by the pressure occasioned by their own weight 
on the plate. Similar spherules, consisting of drops of water, 



Through what successive changes of state may bodies occasionally pass ? 

Give some examples of these changes ? 

Whence arises the difference between a liquid and a solid body? 

Of what action are the particles of elastic solids necessarily suscepti- 
ble ? 

By what force are the particles of liquids held together? 

What constitutes the difference between breaking a solid and separat- 
ing the parts of a liquid ? 

How is the cohesive attraction between the particles of a liquid demon- 
strated ? 



124 HYDRO STATICS. 

are formed by dew or rain on the broad leaves of some kinds of 
vegetables, as those of the common cole-wort or cabbage. If, 
however, the drops become large, as when two or three run toge- 
ther, they spread out at the edges, sinking down, and becoming 
flattened, partly through their own weight, and partly owing to 
the attraction between the water and the surface of the leaf. 

6. The general appearance or figure which liquids assume when 
at rest is the joint effect of the extreme mobility of their constitu- 
ent particles, of the gravitation of liquid masses, and of their at- 
I raction for the solids on which they are sustained. Hence when 
a liquid in any considerable quantity is poured into a vessel of 
any shape whatever, it adapts itself exactly to the internal surface 
of the vessel, the superior or unconfined surface of the liquid form- 
ing a horizontal plane, usually raised a little at the sides or 
border of the vessel, where the liquid is attracted by the contain- 
ing solid with which it comes in contact. 

7. When an immense mass of liquid presents a continued sur- 
face, its form will be a portion of a convex sphere ; because the 
collective gravitation of all its particles towards the centre of the 
earth causes it to partake of the general figure of the terrestrial 
globe. This, indeed, will be the case with comparatively small 
bodies of liquid ; but when it is considered that the radius of the 
sphere, of which any such liquid surface formed a part, would be 
equal to half the diameter of the earth, it must be manifest that 
the difference between the surface of a small portion of such a 
sphere and a horizontal plane would be too inconsiderable to be 
distinguished. Vast collections of water, however, as the open 
sea, afford decisive indications of superficial curvature, among the 
most striking of which is the fact that when a vessel first comes 
in sight its masthead alone is visible, and the lower parts appear 
successively as it approaches the observer, rising as it were out 
of the bosom of the deep. 

8. Among the properties in which liquids differ most remarka- 
bly from gases, is the power of sustaining pressure to a consider- 
able extent, without undergoing any obvious change of volume. 
Common air, steam, and other elastic fluids, as they are termed, 
may be compressed by very moderate force, and on its removal 
they expand to their original dimensions, as may be ascertained 
by squeezing a blown bladder ; but a leather bag or strong bladder 
filled with water, and secured so that none of the liquid can es- 
cape, may be burst by forcible compression, but cannot be made 
to exhibit any sensible degree of contraction. Such indeed is the 

On what three circumstances does the figure assumed by a liquid at 
rest depend ? 

What is the external form of a large mass of liquid ? 

Why is this form taken rather than any other ? 

What sensible evidence is afforded of the spherical form of the earth? 

In what respect do liquids differ essentially from gases ? 

How was water formerly regarded in respect to compressibility ? 

On what experiment was this opinion founded? 



COMPRESSION. 125 

extraordinary resistance of water, when subjected to pressure on 
all sides, that it was long regarded as absolutely incompressible. 
This opinion was partly founded on an experiment made in the six- 
teenth century, by the members of a scientific society at Florence, 
called Academia del Cimento. These philosophers conceived the 
idea of enclosing' a quantity of water in a hollow globe of beaten 
gold, and exposing it to the powerful action of a screw press, 
when it was found that the water was forced through the pores 
of the gold ball or case, standing in drops like dew on its exterior 
surface. But this experiment, can by no means be considered as 
demonstrating the entire incompressibility of the liquid ; for 
though it obviously displayed vast resistance to the compressing 
force, it might have undergone the utmost limit of condensation 
before the exudation took place ; and the experiment was unsatis- 
factory, as affording no means whatever for appreciating the actual 
volume of the water at the moment when it penetrated the solid 
envelope. In fact, nothing more could be inferred from such an 
experiment, but that water is not susceptible of unlimited con- 
densation. 

9. The fallacy of the formerly generally received notion of the 
absolute incompressibility of water was proved by some inge- 
niously contrived experiments by Mr. Canton, a fellow of the 
Royal Society of London, in 1761. He showed that water, in- 
cluded in a glass tube with a large bulb or hollow globe at its ex- 
tremity, expanded and consequently stood higher in the tube when 
placed under an exhausted receiver than when subjected to the 
pressure of the atmosphere, and on the contrary was condensed pro- 
portionally, by pressure equal to the weight of two atmospheres. 
He made similar experiments on spirit of wine, olive oil, and 
mercury, from which it appeared that those liquids undergo con- 
densation, but in different degrees, when subjected to compres- 
sion. In conducting these experiments proper precautions were 
adopted to prevent any inaccuracy arising from variation of tem- 
perature ; and the following table exhibits the results obtained 
when the barometer stood at 29|- inches and the thermometer at 
50 degrees. 

10. Spirit of wine underwent compression amounting to 

0.000,066 of its bulk. 
Olive oil, - - - 0.000,048 
Rainwater, - - 0.000,046 

Sea water, - - - 0.000,040 
Mercury, - - - 0.000,003 
Hence it appears that mercury is far less compressible than water 

What legitimate inference can be drawn from the Florentine experi- 
ment ? 

By whom was the fallacy of the opinion formerly entertained respect- 
ing- the compressibility of water first demonstrated "j 

State the manner in which Canton's experiments were conducted? 

What other liquids besides water were proved by Canton to be com- 
pressible ? 

L 2 



126 HYDROSTATICS. 

11. More recently, experiments on this interesting subject have 
been instituted by M. Oersted, a philosopher who has greatly 
distinguished himself by his scientific researches; and the results 
of his investigations, which appear to have been very carefully con- 
ducted, correspond nearly with those of Canton, the contraction 
of water, under pressure equal to the weight of an additional 
atmosphere, according to the experiments of Oersted, amounting 
to 0.000,045. 

12. Experiments have been undertaken in England with a view 
to ascertain the effect produced by subjecting liquids to compres- 
sing forces of vast energy, far beyond those employed in the re- 
searches of Canton and Oersted. In 1820, an account was laid 
before the Royal Society of London by Mr. Jacob Perkins, of 
some experiments from which he inferred that water had suffered 
a compression of about one per cent, of its bulk by a pressure 
equal to 100 atmospheres ; and in other experiments the com- 
pressing force was augmented to 326 atmospheres, which caused 
a contraction of the liquid to the amount of nearly 3| per cent. 
These results were obtained by including water in the cavity of a 
cannon, fixed vertically in the earth, and driving more water into 
it with a forcing pump ; and corresponding experiments were 
made by sinking water inclosed in a proper apparatus to a great 
depth beneath the surface of the sea, and observing the degree of 
compression it had undergone.* These operations, however, 
could not be regarded as equally accurate with those previously 
described ; though the deductions from them have been corroborat- 
ed by the result of subsequent investigation. 

13. In 1826 Mr. Perkins made public other experiments on the 
compression of water, of which also an account appeared in the 
Philosophical Transactions. The machine he employed was 
composed of a cylinder of gun-metal, 34 inches in length, and 
having an internal cavity to which was adapted a steel pump, with 
a water-tight piston, by means of which water could be injected 
into the body of the cylinder. A lever apparatus was properly 
annexed for the purpose of measuring the degree of pressure ; and 
so adjusted that the number of pounds pressing on its piston indi- 
cated exactly the number of atmospheres equivalent to the degree 
of compression. 

14. That part of the apparatus in which the liquid is enclosed, 
the condensation of which is to be measured, is called by the ex- 
perimentalist a piezometer, j- It consists of a strong glass tube, 
eight inches in length and half an inch in diameter, closed at one 

To what results has Oersted been led by his experiments on water ? 
How many atmospheres of pressure are required to condense water to 
the amount of one per cent, of its ordinary bulk ? 



* See Philosophical Transactions, 1820, and Abstract of Papex'sin Phi- 
osophical Transactions, vol.ii. p. 134. 
fFrom the Greek n*E$», to press, and MsTpot>, a measure. 



COMPRESSION. 



127 



extremity and open at the other. This tube must be carefully 
filled with water freed from air, and being inverted while the 
water is prevented from escaping by the application of a thin 
membrane to its mouth, it must be inserted in a wider tube or 
glass, the upper part of which is filled with water, and the lower 
part with mercury ; the small tube contains a hair-spring pressing 
against its interior surface so as to retain its position when forced 
upward ; and this spring is in contact with a steel disk moving 
freely in the upper tube, and from its inferior weight supported 
by the surface of the mercury below. A frame of strong wire 
retains the small tube in its situation ; and the piezometer being 
thus arranged is introduced into the receiver of the compressor, 
filled with°water at a temperature of 50 degrees, when the pump 
being screwed into its place, any required degree of pressure may 
be applied. When the experiment was carefully conducted it was 
found that water, under the influence of a force equal to 2000 at- 
mospheres, was diminished by 1-12 part, as indicated by the 
situation of the spring.* 

15. The nature of Mr. Perkins's mode of compressing water, wili 




By what part of its original bulk under atmospheric pressure will a 
force of 2000 atmospheres, or 30,000 lbs. to the square inch, condense a 
given mass of water ? 

What is the construction of Perkins's piezometer ? 

* This curious and interesting experiment is exhibitetl dail\,at the Na- 
tional Gallery of Practical Science, in the Strand, London. 



128 HYDROSTATICS. 

perhaps be more clearly comprehended from the annexed figure, in 
which R is the metallic cylinder, G the wider glass tube with a 
quantity of mercury, M at the bottom; g-is the piezometer dipping 
into the mercury below and kept steady by the wire cage C near 
the top ; d is the steel disk, and s the hair-spring to be moved up- 
ward when the water in g is compressed, and the mercury with 
the disk d rises, and to remain and indicate the degree of com • 
pression after the experiment. The use of the force pump P with 
its two valves, v, v, and that of the safety valve V, with the lever 
and weight W serving to determine the force applied, will be 
readily understood. The apparatus of Oersted substitutes a 
strong glass receptacle for the metallic one of Perkins ; and his 
piezometer is a nearly capillary tube in which a thread of mercury 
rises by the compression and forces before it the water with which 
the whole upper part of the tube, (hermetically sealed at top,) 
is filled. Oersted employs to compress the liquid instead of the 
steel pump, a strong thumb-screw inserted into the top of the 
brass cap with which his glass receptacle is closed. He also en- 
closes a thermometer, not hermetically sealed, to mark the degree 
of heat, if any, developed by the effect of mechanical compression. 

16. Though it is manifest, from the preceding statements, that 
liquids undergo great compression under certain circumstances, 
yet the degree of compressibility of such liquids, as water, is so 
inconsiderable when the compressing force is moderate, that no 
sensible effect is produced. Hence in all calculations concerning 
the action of water, at rest or in motion, in ordinary cases, it may 
be regarded as an incompressible fluid. 

17. Liquids in general possess the property of elasticity; but 
like solids, some of them display that property to a greater extent 
than others. When a solid disk, as an oyster-shell or a flat stone, 
is made to strike the surface of water at a small angle, as in the 
sport which schoolboys call making ducks and drakes, the solid 
will rebound from the water with considerable force and frequen- 
cy. So a musket-ball impinging obliquely on water will take a 
zigzag course, en ricochet, as the French express it. Water dash- 
ed against a hard surface, as when it is poured against the side of 
a china basin, or let fall on a plate, shows its elastic force, in 
flying off in drops in angular directions. Experiments on the 
elasticity of drops of water, spirit of wine, or any similar liquid, 
may be made in a shallow wooden box, having its bottom and 
sides thinly covered with any light insoluble powder ; for the drops 
on being impelled against the side of the box, or even against 
each other, will rebound like miniature cricket balls or marbles. 

Might this instrument be employed with advantage to measure the 
compression suffered by water in deep-sea experiments ? Describe the 
arrangement of apparatus employed by Perkins in the compression of 
water. How may water be regarded under the influence of moderate 
changes of pressure ? What evidence is afforded of the elasticity of 
water by the impinging of solid bodies upon its surface ? How may we 
demonstrate the elasticity of drops of water? 



WEIGHT OF LIQUIDS. 129 

18. Mercury is yet more elastic, as might be shown by placing 
a small quantity of it in a little case made by bending at right 
angles the sides of a common playing-card ; and on inclining it so 
as to make the metallic fluid strike one of the raised sides of theh:- 
card, the shining globules would recede with a velocity propor- 
tioned to the violence of the shock. The effects thus exhibited 
appear to be extremely similar to those observed in the case of 
elastic solids. A globule of mercury impinging on a hard sur- 
face becomes slightly flattened, but instantaneously resuming its 
curved figure, it recoils like a bent spring suddenly liberated. In 
some hydraulic operations the elasticity of liquids becomes a pro- 
perty of considerable importance, variously augmenting or modi- 
fying the efficient force of particular kinds of machinery. 

Weight and Pressure of Liquids. 

19. Among the absurd doctrines heretofore generally received, 
but which have been exploded by the light of modern philosophy, 
must be reckoned that of the non-gravitation of the particles of 
liquids on each other. That liquids as well as solids possess 
weight was never denied ; since every one must have learnt from 
experience that a cup or a bucket filled with water would require 
a greater exertion of force to lift it than when the water was re- 
moved. But it was observed that in drawing water from a well, 
so long as the bucket remained under water very little effort was 
required to raise it, while as soon as it emerged from the surface 
of the liquid, the loaded bucket would press downward with a 
force proportioned to the quantity of water contained in it. This, 
and the general observation that heavy bodies were easily raised 
while under water, gave rise to the vague idea that a liquid did not 
gravitate in its own element, and that therefore a body surround'ad 
by any liquid was destitute of weight. 

20. The following experiment sufficiently proves that this is 
not the case. Let a strong phial, with a stop-cock fitted to it, be 
exhausted by means of an air-pump, and the stop-cock being turn- 
ed let it be suspended from one arm c-f a balance, so that it may 
be entirely immersed in a vessel of water, weights being placed 
in the opposite scale of the balance to keep it in equilibrium ; then 
if the stop-cock be opened the water will flow in and fill the phial, 
which will immediately sink, and to restore the equilibrium the 
same weight must be added that would counterpoise the water it 
contains if weighed alone : thus, if the bottle would hold exactly 
four ounces of water, a weight of four ounces would be required 
to make the balance stand even as at first. 

How are analogous experiments on mercury conducted ? 

What appears to be the effect of the impact of a drop of mercury upon 
a hard surface ? 

What opinion was formerly entertained respecting the gravitation of 
liquids upon their own mass ? 

From what circumstance did this idea prohably take its rise ? 

How is its incorrectness conclusively demonstrated? 



130 HYDROSTATICS. 

21. The .apparent diminution of the weight of bodies underwa- 
ter is owing to the particles of the liquid mass gravitating equally 
in every direction ; so that the interior portions of any liquid, or 
of solids immersed in liquids, are subjected to the same degree of 
pressure on all sides; and therefore a body surrounded by water is 
partially supported by it, and consequently may be raised through 
the liquid with greater ease than in the air, a fluid, the relative 
density of which is so very inconsiderable. Liquids are not less 
powerfully affected by gravitative attraction than solids, but they 
exhibit different appearances under its influence, owing to their 
being constituted differently, so that their particles move freely 
and almost independently of each other. 

22. All the constituent particles of a solid are firmly connected, 
and they thus act with combined effect in producing pressure or 
impact ; but a liquid yields to force in any direction, and is liable 
to be separated into small masses, the effect of which is compara- 
tively inconsiderable. A basin of water poured from a great 
height on a man's head would hardly be felt more than a current 
of rain ; but if the contents of the basin, supposing it to hold a 
quart, were suddenly changed to a solid mass of ice, it might oc- 
casion a fracture of the skull. But though a liquid in falling be- 
comes almost dissipated through the resistance of the atmosphere, 
it displays great force when it can be made to act in a continuous 
column. Hence the power of a mill stream in turning large 
wheels either by weight or pressure; and the tremendous violence 
of a cataract, sweeping away great stones or other ponderous 
masses which may present any obstruction to its impetuous 
course. 

23. The effect of a liquid mass when its particles are protected 
from dispersion, and thus enabled to act in concert, like those of 
a solid body, may be amusingly illustrated by means of the little 
instrument called a water-hammer. It consists of a strong glass 
tube, about twelve inches long, and nine or ten lines in diameter, 
having three or four inches of water included in it ; which being 
made to boil and form steam by the application of a proper heat, 
the tube must be hermetically sealed by means of an enameller's 
lamp and a blow-pipe, so that when it becomes cool, a vacuum 
will be formed above the water by the condensation of the inclu- 

How is the apparent loss of weight in bodies immersed in water to be 
explained ? 

To what is the difference attributable between the phenomena exhibit- 
ed by liquids and those observed in solids, when under the influence of 
gravitation ? 

How are the constituent parts of each held together ? 

What simple experiment would illustrate the influence of a change of 
form, in modifying the effect of water ? 

What examples may be cited of great energy displayed by a falling 
liquid } 

By what appai-atus may the percussion of a falling mass of liquid be 
illustrated ? 

Describe the water-hammer. 



PRESSURE OF LIQUIDS. 



3 Jl 



ded steam. On shaking such a tube vertically, the water, rising 
a few inches and sinking suddenly to the bottom of the tube, pro- 
duces a sound like that arising from the stroke of a small hammer 
on a hard body, whence the name of this instrument, the action of 
which depends entirely on the exclusion of the air, so that the 
water moves in a dense mass. 

24. The pressure of liquids extending equally in all directions, 
a liquid mass will have all parts of its surface at the same level, 
whatever be the form of the vessel in which it is contained, so 
long as there is a free communication throughout. 




25. In the preceding figure let A JB represent a glass vessel 
closed except at the two raised extremities, and filled with water 
to a height above the horizontal line; then suppose four dif- 
ferently shaped tubes C, D, E, F, open at both ends, to be in- 
serted in the oblong part of the vessel, with their upper extremi- 
ties not rising so high as those standing at the sides ; it will be 
found that the liquid will pass laterally into the tube C, ascend 
directly in D, and circuitously in E, while it both descends 
and ascends in F, rising equally in all the tubes, and spouting 
out till the water is reduced in the side tubes to the level of the 
summits of the internal ones, when the equilibrium being esta- 
blished the liquid will remain at rest. Thus it follows that any 
number of columns of a liquid, freely communicating, whatever 
may be their respective diameters and figures will always have 
the same vertical height. 

26. Yet though all the particles of a liquid mass will press 
equally on each other, it must be manifest that the collective 
weight will be proportioned to the depth beneath the surface, so 
'hat the bottom of the containing vessel necessarily sustains the 
weight of a column having the greatest vertical height of the 
liquid with an area equal to that of the base itself. 

27. If the vessels A, B, C, D, and E, have water poured into 
tnem in such quantities that it may stand at the same height in 
each, the pressures on their bases respectively will be as the 
several columns marked 1, 2, 3, 4. Hence the amount of the pres- 

What consequence results from the equal pressure of liquids, in regard 
to the height of its surface ? 

What influence has the figure and size of the parts of containing ves- 
sels on the height to which liquids will rise within them respectively ? 

What measures the pressure exercised by a column of liquid on the 
bottom of its containing vessel ? 



132 



HYDROSTATICS. 




sure of any liquid may be ascertained by multiplying the vertical 
height at which it stands by the extent of surface of its base. 
Thus suppose the water in the vessel B to stand at the height of 
four inches, and the area of the base to be eight square inches, the 
pressure will be equal to thirty-two inches of the fluid ; but if the 
water should stand at the same height in the vessel C, having a 
base only half the area of the former, the pressure will be but half 
or only sixteen inches, though the capacity of both vessels may 
be exactly the same. The diameter of a vertical column com- 
municating with an extended base may be relatively inconsider- 
able, as in the vessel E, notwithstanding which it will cause the 
same degree of pressure as a column of the same height with a 
diameter corresponding to the base throughout. 

28. This effect of the vertical pressure of liquids may be vari- 
ously exhibited, and its results are curious and important. Hence 
the principle involving the peculiar mode of pressure of liquid 
masses has been termed the Hydro- 
static Paradox. It may be illustrated 
by the following experiment. Let a 
cup or wide-mouthed jar, filled with 
water, be poised by hanging it to the 
arm of a balance, by loading the oppo- 
site scale with the requisite weights; 
t(iii»iiiiiii[rriiiiiiiiHii»inwii!iiiiiiiiiiiiiiiii'i'iiiiniiri"iiinniii'iiiii'iii!< then alter marking exactty the height 
at which the liquid stands, pour out a part of it, and plunge into 
the midst of the jar a conical block of wood, supporting it with 
the hand or by means of the apparatus represented in the annexed 
figure, taking care that the block shall not touch the sides or bot- 
tom of the jar. If it be plunged just deep enough to raise the 
remaining liquid to the same height as at first, the balance will be 
again exactly equipoised ; and the block may be so large as to 
Jeave only a thin film or hollow cylinder of the fluid without at all 
disturbing the equilibrium. It is of no consequence what is the 
weight or shape of the body introduced, for a piece of cork or a 
blown bladder held in the jar will produce the same effect, if its 
bulk be sufficient to raise the water to the required height.* 

By what mode of calculation may we ascertain that pressure ? 

If a vessel representing the frustum of a cone be filled with liquid, and 
successively placed on its two opposite bases, what will be the relation 
between -the pressures exercised in the two cases ? 

What is meant by the hydrostatic paradox? 

What experiment exemplifies the kind of pressure exercised by liquids? 

How can we prove that the loss of weight from plunging a body into 
water is only apparent ? 

* An ingenious apparatus for drawing water from a vessel in which a 





HYDROSTATIC PRESSURE. 133 

29. There is another striking- mode of illustrating the effect of 
liquid pressure, by means of a'kind of machine called the Hydro- 
static Bellows, a figure of which may be seen in the margin. It 

is composed of two flat boards united at the sides 
by flexible leather, and having a long narrow ver- 
tical tube, communicating with the cavity, with a 
funnel at the top, for the convenience of pouring in 
water or any other fluid ; and a short lateral tube 
with a stop-cock may be added to discharge the 
water occasionally. If now water be poured into 
the long tube it will fill the cavity and consequent- 
ly separate the boards, and b}^ adding more water 
the instrument may be made to support any given 
weight, in proportion to the height of the vertical 
column. Suppose the boards to be about 320 
inches superficial measure, four ounces of water, 

standing at the height of three feet in the tube, will keep the 

boards separated when loaded with 416 pounds. 

30. Two stout men standing on the upper board, one of them 
by blowing into the tube may fill the cavity with air instead of 
water, so as to raise the board on which they stand, and by stop- 
ping the pipe with the finger to prevent the air from escaping, 
they may keep themselves supported. 

31. The force of water pressing on an extended surface by means 
of a small vertical tube may be shown by fixing such a tube in a 
water-tight cask or other close vessel, which, whatever its 
strength, might be burst by filling it with liquid, and adding 
more through the tube, till the weight of the column became too 
great to be supported by the sides of the cask. The effect depends 
wholly on the height of the tube, its diameter being immaterial. 
A hogshead filled with water and exposed to the pressure of a 
column in a narrow tube, twenty feet high, would burst with great 
violence. 

32. Astonishing effects are sometimes produced by the pres- 
sure of water modified in the way already described. As when a 
shallow body of water is collected in a close cavity under ground, 

Describe the constitution, and explain the principle, of the hydrosta- 
tic bellows ? 

In what manner might the same principle be applied to maintain a re- 
gular blast of air for the blow-pipe ? 

In what manner do we demonstrate the importance of height of co- 
lumn to the effect of liquid pressure ? 

In what manner may the effect of hydrostatic pressure on portions of 
the earth's surface be manifested ? 

solid has been made to float until the liquid has the same level.as at first, 
and then weighing the quantity drawn out against the solid which had 
been floating, proves the same general position as the arrangement above 
described. It moreover shows that the weight lost by the solid, and the 
upward pressure of the liquid which is the cause of that loss, are both 
equal to the weight of water so displaced. — En. 

M 



134 



HYDROSTATICS. 



if a narrow opening be made from a higher surface communicating 
with the cavity, and it should become filled by rain or snow water, 
whatever might be the form of the aperture, if it was water-tight, 
as soon as the communication was effected between the tube-like 
opening and the cavity, pressure would take place in every di- 
rection, in a degree proportioned to the vertical height of the open- 
ing and the area of the cavity ; in consequence of which the 
superincumbent mass might be rent from its foundation, and a large 
building or even a mountain might be overthrown, as by an earth- 
quake. 

33. The principle of hydrostatic pressure was discovered, or at 
least first satisfactorily demonstrated, by the celebrated Pascal, 
about the middle of the seventeenth century ; and he showed how 
an engine might be constructed, acting through the force of a 
column of water, by means of which one man pressing on a small 
piston might counterbalance the efforts of one hundred men 
brought to bear on the surface of a large piston. Yet notwith- 
standing the distinct description of what the ingenious discoverer 
terms "a new machine for multiplying forces to any required 
extent," *more than a century and a 
half elapsed before the idea was fully 
developed, and applied to practical 
purposes, by Mr. Bramah, the engi- 
neer, in the construction of his hydro- 
static press. 

34. This machine consists of a 
solid mass of masonry or strong wood- 
work, E F, firmly fixed ; and con- 
nected by uprights with a cross-beam. 
B represents a strong table, moving 
vertically in grooves between the up- 

1 1 rights, and supported beneath by the 

piston A, which rises or descends within the hollow cylinder L, 
and passes through a collar N, fitting so closely as to be water- 
tight. From the cylinder passes a small tube with a valve open- 
ing inwards at I, and D is a lever which works the piston of the 
small forcing-pump C H, by which water is drawn from the 
reservoir G, and driven into the cylinder L, so as to force up its 
piston A. At K is a valve, which being relieved from pressure, 
by turning the screw which confines it, a passage is opened for 
the water to flow from the cylinder, through the tube M, into the 
reservoir G, allowing the piston to descend. 

35. The effective force of such a machine must be immensely 

Who first demonstrated the principle of hydrostatic pressures accord 
ing to the height of column ? 

What application did Pascal propose to make of the principle of pres- 
sure according to the area of the base of the containing vessel ? 

By whom, and at what period, was the idea of Pascal fully realized ? 

What is the construction of Bramah 's press ? 

* Pascal de l'equilibre des liqueurs, edit. ~, 1GG4, ch. ii. 




PRESSURE OF LIQUIDS. 135 

great, combining- as it doe? the advantages of solid and liquid 
pressure. The amount of the latter is to be estimated by the 
relative diameters of the two pistons ; so that if the piston H be 
half an inch in diameter and the solid cylinder or piston A one 
foot, the pressure of the water on the base of the piston A will be 
to the pressure of the piston H on the water below it, as the_ 
square of 1 foot or 12 inches, 12 X 12 = 144, to the square of ^ 
an inch, .5 X .5 = .25; that is as 144 square inches, to f of a 
square inch, or in the ratio of 576 to 1. To this must be added 
the advantage afforded by the lever handle of the forcing-pump, 
depending on the relative lengths of its arms ; and supposing the 
power to be thus increased tenfold, the effect of the machine will 
be augmented in that proportion, or will become as 5760 to 1. 

36. As the hydrostatic press acts with a comparatively trifling 
degree of friction, it may be made to produce an infinitely great 
amount of pressure ; its efficiency in fact being limited onty by 
the measure of the strength of materials employed in its construc- 
tion. Some idea of the power of this engine may be derived from 
the statement that with such a press, only the size of a common 
tea-pot, a person may cut through a thick bar of iron with no more 
effort than would be required to slice off a piece of pasteboard 
with a pair of shears. It has been used in making experiments 
on the tenacity and strength of iron and steel, being applied so as 
to tear asunder solid rods or bars;* and in packing bales of cotton 
or trusses of hay, it has been employed to compress them to con- 
venient dimensions for stowage on board ships. 

37. The principle of hydrostatic pressure has been ingeniously 
applied to a purpose of great practical utility by Dr. Arnott, in 
the contrivance of a hydrostatic bed for invalids. It is so con- 
structed as to keep the body of a person reposing on it, sustained 
by a mattress on a liquid surface, yielding freely in every direc- 
tion, and therefore entirely exempted from any irregular pressure : 
thus the irksomeness, as well as the serious evils caused by con- 
finement to one position for a long time, and the consequent inju- 
ries which persons enfeebled by disease sometimes incur, may be 
wholly prevented. 

38. The pressure of water or any other liquid against the bot- 
tom of a vessel in which it is contained may be regarded as the 
common effect of gravity, which acts in the same manner on solid 

What method will enahle us to estimate the advantage of a Bramah's 
press of known dimensions ? 

What advantage has the hydrostatic press over the screw press and si- 
milar machines ? 

What limits the efficiency of this apparatus ? 

What remarkable applications of the hydrostatic press illustrate its 
force and usefulness ? 

What is the construction of Arnott's invalid bed ? 

In what respects does the pressure of a liquid within a containing vessel 
differ from that of a solid under the same circumstances? 

* See Encyclopedia Metropolitans. — Mixed Sciences, vol. i. p. 70. 



136 



HYDROSTATICS. 



bodies ; but liquids not only press on the surface beneath, but 
also press upward, with a degree of force proportioned to the depth 
of the vertical column and the extent of surface against which the 
pressure is exerted. 

39. Take a very narrow glass tube open at both ends, and dip 
the lower extremity beneath the surface of quicksilver, so that a 
small portion of it may rise into the bottom of the tube ; then 
stopping the upper extremity carefully with the finger, lift the 
tube, and holding it vertically, plunge the open end into a deep 
jar filled,, with water, when it will be found that the pressure of 
that liquid from below upwards will not only keep the quicksilver 
suspended, when the finger is removed from the top of the tube, 
but on letting it sink gradually in the jar, the quicksilver will rise 
to a height bearing a certain relation to the depth of the lower end 
of the tube beneath the surface of the water. 

40. Let a circular brass plate A B be adapted to 
w the bottom of a glass cylinder and fitted accurately 

by grinding, or by covering its upper surface with 
moist leather, so that when the cylinder is immersed 
in the jar of water F F, and the plate is held by the 
string E close to the bottom of the cylinder, none of 
the liquid can enter it. If then it be immersed to 
such a depth that the weight of the vertical column of 
water which it displaces shall be equal to the weight 
of the brass plate, the latter will remain suspended 
though the string be let go, the upward pressure of 
the water being sufficient to keep the plate from fall- 
ing. 

41. In estimating the lateral pressure of liquids 
the vertical height must be taken into the account ; 

since the effective force with which a liquid acts against any given 
point in the side of the containing vessel will depend on the depth 
of that point beneath the surface of the liquid. 

42. This will appear from the man- 
ner in which water flows from apertures 
in the side of a cistern, as the velocity 
of the stream will always be exactly 
proportioned to the distance of the point 
of discharge from the superior surface, 
and the consequent degree of pressure 
which takes place. Suppose a vessel 
A to be filled with water, and to have 
I! T three tubes or pipes, B, C, D, of equal 
If length and diameter, fitted into lateral 
I 1 apertures at different heights ; then if 

How are we to account for the rising of a drop of quicksilver in a nar- 
row tube, when plunged into water ? 

To what depth must a metallic plate, ground to fit the open mouth 
ot a glass tube, he immersed in a liquid before the upward pressure of 
the liquid will support the plate ? What is to be taken into the account 
in estimating the lateral pressure of liquids i 





LATERAL PRESSURE OF LIQUIDS. 137 

the liquid were suffered to flow from the pipe D alone, the others 
being- stopped, a greater quantity of water would be discharged in 
a given time than by the pipe C alone, and a greater quantity- 
would issue from the latter in the same time than by the pipe B 
only; the water being kept at the same level, so as to maintain an 
equality of pressure during the whole time it was flowing. And 
if all three pipes were opened together, the water would spout to 
a greater distance from the pipe D than from either of the others. 

42. The pressure against one side of a cubical vessel filled with 
liquid will be equal to half the pressure against the bottom of the 
vessel. Hence in a quadrangular cistern the amount of pressure 
against its sides may be found by multiplying the number of 
square feet contained in that part of the sides beneath the surface 
of the liquid by half the height at which it stands ; and therefore 
if the extent of the lateral area in contact with the liquid be double 
that of the bottom of the containing vessel, the pressure on the 
sides will be equal to that on the bottom. Thus a calculation may 
be made of the pressure of water against a dam, wear or floodgate, 
by ascertaining the superficial measure of the surface against 
which the water presses, and multiplying it by half the depth of 
the vertical column. Suppose a dam to be built across a body of 
water 6 feet in depth and 14 feet wide, the extent of the surface 
subjected to pressure would be 84 square feet, which being mul- 
tiplied by 3, half the depth, the product 252 would denote the 
quantity of cubic feet of water pressing on the dam. In the same 
manner may be ascertained the degree of pressure of a liquid 
standing in an upright cylinder, as a leaden pipe or cistern ; by 
multiplying the number of square inches or feet in the curved sur- 
face by half the depth of the liquid : and this method may be 
extended to all cases of the lateral pressure of liquids, whatever 
be the shape of the containing vessel or cavity. 

43. When a liquid presses on any surface there will be a cer- 
tain point at which a degree of pressure being applied equal to 
the entire pressure of the liquid would produce exactly the same 
effect ; or if such equivalent pressure were applied to that point, 
but in the contrary direction, it would neutralize the pressure of the 
liquid on the opposite surface : that point is therefore called the 
centre of pressure. It corresponds exactly with the centre of 
percussion in solids, which in most, but not all cases, coincides 
with the centre of oscillation. To ascertain the situation of this 

To what is the distance to which liquids will spout from an aperture in 
a containing vessel always proportioned ? 

What relation exists between the velocity of flow and the height of 
the aperture ? 

How may we estimate the pressure against the side of a cubical con- 
taining vessel filled with any liquid ? 

To what practical purposes may this method of calculation be applied ? 

How is the amount of pressure on a cylindrical tube ov vessel filled 
with liquid to be determined ? 

What is meant by the term ceiifre of pressure in liquid masses ? 

With what point in solid masses does the centre of pressure correspond ? 
m 2 



138 HYDROSTATICS. 

point often becomes an object of importance ; since it will indi- 
cate the most efficient means for sustaining 1 a floodgate or any 
similar surface against the pressure of a bod}' of water. The 
position of the centre of pressure must depend on the figure of the 
surface and the depth of the head of water. Supposing the sur- 
face to be a perpendicular parallelogram, the centre of pressure 
will be at two-thirds of the distance from the level of the water to 
the bottom; and if the figure of the surface be an equilateral tri- 
angle, at three-fourths of the distance from the vertex to the base. 

44. On the principle of the lateral pressure of liquids may be 
estimated the pressure sustained by solids immersed at any depth 
beneath a liquid surface. Thus, if it be required to find the pres- 
sure which a diver sustains when he has descended in water to 
the depth of 32 feet, or rather to such a depth that the centre of 
gravity of his body may be exactly 32 feet beneath the surface of 
the water ; then as the extent of surface of a human body, at a 
medium, may be estimated at 10 square feet, the product of that 
number multiplied by 32 will give the quantity of water in 
cubic feet, the weight of which must be sustained by the diver at 
the depth just stated. Now as one cubic foot of water weighs 
1000 ounces avoirdupois, the weight of 320 cubic feet will be 
320,000 ounces or 20,000 pounds.* 

45. The equability of the pressure in every direction renders 
such an immense weight supportable ; though it occasions con- 
siderable inconvenience to persons learning to dive, from the 
intense pain caused by the pressure of the water on the drums of 
the ears, even at the depth of 18 feet below the surface. It ap- 
pears probable that diving in very deep water, at length, has the 
effect of rupturing the membrane called the drum of the ear, after 
which pain in that organ is no longer felt by the diver ;| but there 
must be a limit to the depth to which the most experienced diver 
can descend, since at a very great depth the compressing force of 
the liquid mass would be so augmented as to expel entirely the 
air that had been retained in the cavities of the chest and head, 

On what circumstance will its position depend ? 

At what point in a floodgate in the form of a rectangular parallelo- 
gram might a single force on the side opposite to that pressed by the 
water be applied, so as to resist the whole pressure of the liquid within ? 

How may we find the amount of pressure upon the body of a diver, 
when at a given distance below the surface ? 

Why is not a person crushed by the weight of liquid above him, when 
placed many feet below the surface of water ? 

What peculiar sensation is felt at first by persons unaccustomed to deep 
diving ? 

What is supposed to take place when the inconvenience at first felt is 
found to cease ? 

Why may not a man descend to any depth below the surface of water? 

* The manner of ascertaining the weight of any body relatively to its 
bulk will be described in the next section, in treating of specific gravity. 
t See Hardy's Travels in the Interior of Mexico. London, 1829. 




THE SPIRIT LEVEL. 139 

and contract the bulk of the whole body in such a manner as to 
render ascent to the surface no longer practicable. 

47. The uniform pressure of liquids in every direction, and the 
consequent equality of action and reaction among; the parts of 
liquid masses cause them to assume a level surface under all cir- 
cumstances. This property of liquids has been advantageously 
employed in the construction of instruments for ascertaining - the 
relative heights oi' any given points, as in taking levels in survey- 
ing, and in various operations in which it is requisite to deter- 
mine the accuracy of a horizontal 
plane. Such an instrument may 
consist of a glass tube of consider- 
able length, as represented in the 
margin, open at both ends, which 
must be raised or turned upward to 
the same height ; and the tube being 
filled with water or mercury, when 

it is placed in a horizontal position, the liquid will stand at the 
same level on both sides. Upon the open surfaces of the liquid 
must be placed floats, each carrying upright sights with cross- 
wires, which standing at right angles to the length of the instru- 
ment, when it is properly adjusted, the intersections of the wires 
will be situated in a horizontal line; and consequently on look- 
ing through the sights at any distant object it can only be seen 
exactly opposite the intersections of the wires when it happens to 
be in the same level. 

48. The spirit level, an instrument adapted to the same pur- 
poses with the preceding, consists of a glass tube, closed at both 
ends, and filled with alcohol, except a very small space occupied 
by a bubble of air, which, in whatever situation the tube may be 
placed, must rise to the highest part of it. When, therefore, the 
tube is fixed in a horizontal position, the bubble will stand pre-* 
cisely in the centre of the tube and in contact with its surface. 
Such a level may be used like the water-level, above described, 
for ascertaining the accuracy of a horizontal plane ; or it may be 
mounted in a frame with moveable sights adapted to a quadrant, 
by means of which the angular distances of objects may be deter- 
mined with the utmost degree of correctness. 

49. The property which liquids possess of preserving an exact 
level in different tubes or vessels communicating with each other 
is of the highest importance, as indicating an obvious mode of 
conducting water from one situation to another. Thus from a lake 
or reservoir this useful fluid may be conveyed in pipes or tunnels 
underneath streets and buildings to any given distance, and sup- 
plied to the different quarters of a town or city, at any height not 
exceeding that of its source. The whole amount of the daily 

What is the general construction of liquid levelling instruments ? 
What is the form and use of the spirit level ? 

On what principle are we enabled to conduct water under ground, and 
through irregular tubes ? 



140 HYDROSTATICS. 

supply of water to the cities of London and Westminster appears 
to be nearly 26,000,000 gallons, more than half of which is derived 
from the Thames ; and as most of it is delivered at heights much 
above the level of the river, it is necessarily raised by artificial 
pressure by means of steam-engines. 

50. Though w T ater and similar liquids may be transferred to any 
imaginable distance through a series of communicating tubes bent 
into numerous angles, descending and ascending, and made to 
issue freely at a height nearly equal to the source ; yet it is found 
in practice that obstruction, arising from the friction of the liquid 
against the sides of the tubes, especially where they form acute 
angles, and from the accumulation of bubbles of air in long nar- 
row tubes, may cause great inconvenience ; and hence large pipes 
are more advantageously employed than smaller ones, and aque- 
ducts or open conduits are to be preferred in some situations. 

51. In the south of Europe may be seen the remains of stupend- 
ous aqueducts constructed by the ancient Romans, forming open 
canals supported by numerous arches passing across wide valleys, 
and exhibiting even in decay striking memorials of the architec- 
tural skill and industry of those to whom they owe their origin. 
From these magnificent works on which such immense labour 
must have been bestowed for the purpose of conducting water on 
one descending plane, it has been hastily inferred that the an- 
cients were entirely ignorant of the effect of hydrostatic pressure ; 
and of the means of making water rise to the height of its source 
after passing through a lower level. But this notion is utterly 
erroneous, for in the great work of the celebrated naturalist, Pliny 
the elder, it is expressly stated that water will always rise to the 
height of its source ; and he adds that tubes of lead must be used 
to carry water up an eminence.* Passages to the same effect 
might be adduced from other ancient writers, containing plain 
allusions or direct statements relative to the consequences of the 
pressure and flow of water. Indisputable evidence that the an- 
cients were not ignorant of this principle has been afforded by the 
researches made among the ruins of Pompeii, where the remains 
of fountains and baths show that the inhabitants of that cit} r , 
which was destroyed in the reign of the Emperor Titus, were not 
unskilled in the means of causing water to ascend through pipes 
and conduits. The reason why the Romans did not adopt the 
method of conducting water through large tubes was chiefly 
because they were unable to construct such tubes as would be 

Of what nature are the impediments to the motion of liquids in con- 
duit pipes ? 

In what manner were the ancients accustomed to conduct water from 
a distance into their cities? 

What evidence have we that the ancient Romans understood the prin- 
ciples of hydrostatic pressure as applicable to subterranean conduits ? 

* Plinii Hist. Natural, lib. xxxvi. cap. vii. See Leslie's Elem. of Nat. 

Phil os. pp. 411 — 413. 



RAIN. 141 

water-tight when exposed to the pressure of a considerable 
column ofliquid. Their wa*er-pipes were made of lead, earthen- 
ware, or wood, and were in many respects inferior to those used 
in modern times. 

52. Some of the most remarkable phenomena of nature are 
owing 1 to the tendency of liquids to form coherent masses, to 
become extended over the surfaces of solids, and to flow in any 
direction till they find a common level. Water is the most abun- 
dant of all liquids, and if we trace its operations under the seve- 
ral forms of rain, springs, fountains, running streams, lakes, or 
rivers, communicating with the extended ocean, the peculiar pro- 
perties which constitute the distinctive character of liquid bodies 
will be recognized in the effects which they produce. Some 
notice has already been taken of the different states of aggrega- 
tion which water assumes when exposed to certain degrees of 
temperature, being expanded or converted into vapour by heat, 
and condensed by cold.* It may be considered as making its 
first appearance as a liquid in the form of falling rain, which con- 
sists of drops of water recently produced by the condensation of 
aqueous vapours. 

53. "The drops of rain vary in their size, perhaps from one 
twenty-fifth to one-fourth part of an inch in diameter. In parting 
from the clouds, they precipitate their descent till the increasing 
resistance opposed by the air becomes equal to their weight, when 
they continue to fall with a uniform velocity. This velocity is, 
therefore, in a certain ratio to the diameter of the drops ; hence 
thunder and other showers in which the drops are large pour down 
faster than a drizzling rain. A drop of the twenty-fifth part of 
an inch, in falling through the air, would, when it had arrived at 
its uniform velocity, only acquire a celerity of eleven feet and a 
half per second ; while one of one-fourth of an inch would acquire 
a velocity of thirty-three feet and a half."f 

54. Experimental inquiries have frequently been instituted as 
to the quantity of rain which had fallen at any particular place 
during a certain period. An estimate of the amount of aqueous 
fluid discharged from the atmosphere might be formed from 
observing the quantity of rain-water descending on the roof of a 
house or any other building, provided the whole could be collected 
and measured before any portion of it had been dissipated by 
evaporation, and an exact measurement could also be obtained of 
the superficial area of the surface on which the rain had fallen. 

Why did not the ancients carry all their aqueducts beneath the surface 
of the ground ? 

What limits the velocity of water descending in the form of rain ? 

To what is the resistance of the air to falling drops of water propor- 
tioned ? 

How might an estimate be formed of the amount of water descending 
annually over the surface of a country ? 

* See Mechanics, 54. f Leslie's Treatise on Heat and Moisture. 



142 HYDROSTATICS. 

There are some situations in which this plan might be executed 
without much difficulty. 

55. But a more generally applicable, though perhaps less satis- 
factory method of ascertaining the daily, weekly, monthly, or 
annual fall of rain, in any situation, is by means of an instrument 
called a pluviameter, or rain-gauge. This instrument has been 
variously constructed, and the different forms which have been 
■.ecommerided may each have their particular advantages ; but the 
general object of all of them is the collection of rain falling on an 
area of known extent, as a few square inches, and providing 
for its accurate measurement. Below is represented a rain- 
guage which has at least the merit of simplicity, as showing, on 
inspection, the quantity of rain-water which may have fallen on a 

certain area during any given time. It con- 
sists of a quadrangular-topped funnel, A, 
the opening of which may be ten inches 
square, terminating below in a reservoir B. 
Through the neck or opening between the 
funnel and the reservoir is inserted the gra- 
duated rod C, to which is adjusted the ball 
D, made of cork or light wood, so that it 
may float on the surface of the v/ater in the 
reservoir, and the upper part of the rod being 
marked with divisions into inches and parts 
of an inch, will indicate by its ascent the 
depth of water in the reservoir. The stop- 
cock E serves to let off the water after its quantity has been noted, 
or at any stated periods. A more simple instrument consists of a 
conical vessel about 8 or 9 inches high and 5 inches in diameter, 
placed in a convenient frame and furnished with a rod, graduated 
progressively to correspond to the varying size of the cone. 

56. According to the observations of Mr. Daniell, the average 
quantity of rain which falls in the neighbourhood of London, in 
the course of a year, amounts to 23.1 inches ; the greatest quan- 
tity falling generally in the month of July, and the least in Febru- 
ary ; and the whole quantity falling during the first six months 
being not much more than half that in the last six months of the 
year.* 

57. Leslie has remarked that in general twice as much rain 
falls on the western as on the eastern side of the island of Great 
Britain, and that the average quantity may be reckoned at 30 
inches. According to this estimate, the whole discharge from 
the clouds in the course of a year, on every square mile of the sur- 
face of Great Britain would at a medium be 1,944,633, or nearly 

How is the rain-gauge constructed and applied ? 

What depth of rain generally falls in London in the course of a year? 



* Meteorological Essays and Observations. By J. F. Daniell, P. R. S 
2d edit. 




ORIGIN OF SPRINGS. 143 

2,000,000 tons. This gives about three thousand tons of water for 
each English acre, a quantity equal to 630,000 imperial gallons.* 

58. It may he questioned whether the very limited extent of 
any observations which can be made by means of rain-guages 
affords ground for perfect confidence in the results they afford ; 
and hence wherever experiments can be prosecuted on a larger 
scale it is desirable that they should be recorded ; as the conclu- 
sions already obtained might thus be either confirmed or cor- 
rected. 

59. There is one singular circumstance attending the fall of 
rain calculated to throw some doubt on the absolute accuracy of 
the common mode of observation, which is, " that smaller quan- 
tities have been observed to be deposited in high than in low 
situations, even though the difference of altitude should be in- 
considerable. Similar observations have been made at the sum- 
mit, and near the base of hills of no great elevation. Rain-guages 
placed on both sides of a hill at the bottom, always indicate a 
greater fall of rain than on the exposed top."* 

60. It appears, however, that larger quantities of rain fall on 
extended tracts of elevated ground than at the level of the sea; 
but that at stations abruptly elevated above the surface of the 
earth the amount diminishes with the ascent. The mean annual 
fall of rain at Geneva, as calculated from observations during 
thirty-two years, amounts to 30.7 inches; and on the Alps, at the 
Convent of the Great St. Bernard, the mean of twelve years is 
60.05 inches. According to M. Arago, who has traced a pro- 
gressive decrease in the annual amount of rain from the equator to 
the poles, not less than 123.5 inches fall in a } r ear on the Malabar 
coast, in latitude 11^ deg. N. ; while in latitude 60 deg. the 
quantity is reduced to 17 inches. 

61. The water that falls from the clouds as well as that derived 
from melted snow and similar sources, if the surface with which 
it comes in contact happens to be loose and porous, will sink into 
the bowels of the earth, penetrating in any direction till it meets 
with a stratum of clay, or some other dense and almost impervious 
substance, which may cause it to accumulate and form subterrane- 

IIow great a weight of water has Leslie supposed to fall on a square 
mile of the surface of Great Britain. 

What is found to be the relative quantity of rain falling in high and low 
stations ? 

How are the quantities of rain found to vary on high table lands, and at 
the level of the sea ? 

What remarkable example of this variation can be adduced ? 

What are the relative quantities of rain falling in the torrid and in the 
temperate zones respectively p 

Explain the manner in which water reaching the earth from the clouds 
is eventually disposed of? 

* Leslie on Heat and Moisture ; see, also, Proceedings of the British 
Association at Cambridge, 1833, for a report of experiments made at 
York.— En. 



144 HYDROSTATIC?. 

ous lakes or reservoirs, the contents of which occasionally are 
-aised to the surface in various situations by hydrostatic pressure. 
Thus sometimes in digging wells it is necessary to penetrate to a 
great depth before water can be obtained, but at length when the 
source is found the water rises with such rapidity in the shaft 
that has been opened as scarcely to leave time for the well-sinkers 
to make their escape from the ascending column. 

62. The term Artesian wells has been recently applied, espe- 
cially in France, to wells formed in the manner just described, 
by the ascent of water through openings made by boring down 
and introducing tubes which traverse the superior strata, and com- 
municate with subterraneous springs or reservoirs, from which 
the water rises through the tubes by hydrostatic pressure, nearly 
or quite to the surface; constituting in the latter case perpetual 
fountains, such as occur on the eastern coast of Lincolnshire, 
England, where they are called Blow Wells. The)' are also fre- 
quent in Artois, in the Netherlands, and hence they have derived 
the appellation of Artesian wells, from Artesium, the ancient 
name of that countn\* 

63. "Water collected in subterraneous passages by infiltration 
sometimes passes below the bed of the sea, and forms a sort of 
Artesian fountains, which flow at intervals depending on the ris- 
ing and falling of the tide. A remarkable ebbing and flowing 
stream of this kind was discovered in 1811, by boring in the har- 
bour of Bridlington in Yorkshire ;t and submarine fountains have 
been met w T ith at the mouth of the Rio los Gartos, in South Ame- 
rica, at Xagua, in the Island of Cuba, and elsewhere. ^ 

61. By means of such underground canals formed by nature, 
streams of water and even great rivers, after sinking into gulfs 
and cavities in the earth, make their appearance again at the sur- 
face, in some cases far from the spots where they descended. § 
Gulfs of this kind, in which rivers anfl rivulets lose themselves, 
occur in the Alps of Jura, and other limestone mountains ; and 
where the upper surface consisting of a bed of tenacious clay pre- 
vents the absorption of the rain-water by the soil, openings into 
the more porous strata beneath whether natural or artificial, may 

What evidence have we of the existence of extensive collections of 
water under the surface of the ground ? 

To what is the term Artesian wells applied ? 

What is the origin of that term ? 

In what remarkable situation has the formation of Artesian wells been 
occasionally prosecuted ? 

* See Notice of a Lecture on Geology, by Dr. Buckland, in the Re- 
port of the British Association, vol. i. pp. 100, 101. 

t See a Paper bv John Storer, M. D. in the Philosophical Transactions, 
for 1815. Abst. of Papers in Phil. Trans, vol. ii. pp. 6, 7. 

\ Numerous Artesian wells, both salt and fresh water, have been formed 
in the United States. — Ed. 

§ See Humboldt's Travels, vol. ii. p. 31'J. 



CATARACTS. 145 

be made the means of converting a marshy waste into a fertile 
plain.* 

65. When rain falls oh the summits or elevated sides of hills 
and mountains, if the surface be solid rock or clay, the liquid, by 
its natural tendency to flow till every part of its exposed surface 
has attained a common level, collects in rills, which find or form 
for themselves narrow channels, through which the water descends 
to the plains below ; there the confluence of springs from various 
sources produce lakes or rivers, which in general ultimately com- 
municate with the ocean, or with some great inland sea, like the 
Caspian or the Lake of Aral, both which are below the level of 
the Mediterranean ;| and other lakes which have no outlet must 
be situated in valleys or basin-shaped cavities, either below the 
sea-level, or surrounded completely by walls of rock or compact 
earth, which prevent the egress of the liquid mass. 

66. Rivers in their passage to the deep sometimes form grand 
and beautiful cataracts and waterfalls, w r here the collective stream, 
after being confined in a narrow channel, bursts abruptly over a 
precipice with astonishing force, dashing on the lower surface, 
and rising again in clouds of misty spray. Such are the famous 
Falls of Niagara, formed by the water of Lake Erie ; the Cataract 
of Tecquendama, on the Rio Bogota, in South America, described 
by Humboldt; the Fall of the Rhine at SchafFhausen ; and the 
cataracts of the Nile, at Syene, now Assouan, in Upper Egypt. 

67. The currents, which have been thus rushing with impetu- 
ous force over the same surfaces for successive ages, cannot but 
have had a considerable effect even on the hardest rocks of which 
their beds are formed ; and hence the heights from w T hich these 
torrents descend being gradually worn down, alterations take 
place, and the cataracts must at length lose much of that formid- 
able and impressive appearance they now exhibit. It is owing 
no doubt to such changes that the descriptions given by ancient 
travellers and geographers of some of the most remarkable cata- 
racts by no means correspond with their present state. 

68. Rivers formed by nature are running streams, whose velo- 
city depends on the inclination of the surface of the country 
through which they pass. They have in various ages and in dif- 

In what instances is water known to have collected in basins below the 
level of the sea ? 

What influence are cataracts known to exercise on the rocks over 
which they descend ? 

Why are the accounts of ancient travellers not always verified by the 
present appearance of cataracts ? 

On what does the velocity of natural streams depend ? 

* See an account of the draining of the Plain of Palans, near Mar- 
seilles', by sinking shafts from the surface into the cavernous strata be- 
low, which conveys water through subterraneous channels to the harbour 
of Mion, near Cassis, forming spouting springs, or Artesian fountains. — 
Arcana of Science for 1832, pp. 235, 236 ; from Herieart de Thury. 

t See the Report of the British Association at York, p. 239. 

N 



J 46 HYDROSTATICS. 

ferent parts of the world been made the means of intercourse by 
inland navigation between distant places. For this purpose, how- 
ever, they are but imperfectly adapted ; since, besides the obsta- 
cles arising from rapids and cataracts, there must always be 
difficulty in ascending the stream of a river proportioned to the 
rapidity of the descending current. Hence in many countries 
navigation for the purpose of internal communication is in a great 
degree confined to the larger rivers and tide-ways, and to the 
numerous artificial canals which have been constructed chiefly 
since the middle of the last century ; and the smaller natural 
streams, crossed by wears, mills, and manufactories of various 
descriptions, may thus be most effectively rendered subservient to 
the promotion of national industry and wealth. 

69. A navigable canal usually consists of several continuous 
bodies of water, sometimes of considerable longitudinal extent, 
and each one having a perfectly level surface, the water being at 
rest. In a country intersected by numerous mountain ridges and 
valleys, the formation of a long unbroken line of canal must in 
general be attended with difficulties, and can seldom be effected 
at all except by erecting massive aqueducts supported on arches, 
and stretching from one point to another over the lower grounds, 
and elsewhere by carrying subterraneous galleries or tunnels 
through intervening hills. 

70. Canals, however, generally consist of several longitudinal 
basins at different levels, and to preserve or rather occasionally 
to form communications between these, for the passage of vessels, 
locks are constructed wherever a variation in the level takes place, 
and thus vessels may be raised or lowered, according to circum- 
stances. Locks are nothing more than small basins, with flood- 
gates at each end, placed across the canal, from side to side, and 
thus including a portion of its water between them. To transfer 
a vessel from the higher to the lower level, the water in the inter- 
vening lock must be raised, by opening sluices at the bottom, to 
the height of the upper level, then the floodgates on that side 
being opened, the vessel is to be drawn into the lock, the gates 
through which it has passed are to be shut, and the water in the 
lock suffered to sink through sluices to the level of the lower part 
of the canal, and the lower floodgates then being opened the 
vessel may proceed on its passage till it reaches the next lock, 
where the same process must be repeated. The transfer of a ves- 
sel from a lower to a higher level is effected by the contrary 
operation of raising the water in the lock, instead of sinking it, 
while the vessel remains inclosed in it. 

71. The passage of vessels in either direction through a lock 
cannot take place without the loss of a considerable quantity of 

What circumstance limits the usefulness of rivers for purposes of na- 
vigation ? 

Of what do artificial canals commonly consist? 

In what manner is a communication effected from a reach of canal at 
one level to that at another ? 



SPECIFIC GRAVITY. 147 

water, which must in each case he allowed to escape from the 
higher to the lower level of the canal. Where the supply of water 
therefore is not very copious, and more especially when the appli- 
cation of artificial means is requisite to obtain it, the loss becomes 
a serious inconvenience, and source of expense. This has led to 
different schemes for the conveyance of canal-boats from one level 
to another, without any expenditure of water. 

72. One method of effecting this object is by means of a sus • 
pension-lock or moveable basin, containing a body of water suf 
ficient to float a canal-boat, and capable of being alternately raised 
to the higher and depressed to the lower level of two correspond- 
ing parts of a canal, separated from each other by floodgates, with 
a space between them in which the suspended basin might be 
raised or lowered, so as to take in and discharge the boat. This 
scheme does not appear to have been put in practice, at least not 
on an extensive scale ; and from the complication of the machinery 
requisite, it would probably be found liable to insurmountable ob- 
jections. In some situation, the basin terminates at a certain 
point, and another basin comm«ncing at a lower level, boats are 
transferred from one basin to another by inclined planes. 



Specific Gravity. 

73. The terms Density and Specific Gravity have been re- 
peatedly introduced in the preceding pages; and their general 
signification has been in some degree elucidated already. It will 
however be necessary now to explain somewhat more fully the 
signification of those terms, not only as applicable to liquid bodies, 
but likewise with reference to solids and gases ; and to describe 
the means by which the specific gravity of any substance may be 
ascertained. 

74. In describing the effects of hydrostatic pressure, we have 
hitherto considered them as owing to the presence of a single 
liquid; the illustrations of the principles of the science now under 
review having been chiefly drawn from the phenomena exhibited 
by water alone, in several situations and circumstances, as afford- 
ing results more simple and uniform than those which are observed 
when different liquids are placed in contact with each other, and 
when their combined pressure on solids as well as their mutual 
action must be modified accordingly. 

75. It has been sufficiently demonstrated that a single liquid, as 
water, will always stand at the same height in two or more open 

What disadvantage attends the transfer of boats from one level to an- 
other by means of locking ? 

What methods have been proposed or employed to obviate the loss of 
water in the transfer of boats ? 

To how many classes of bodies are the terms density and specific gra- 
vity applicable ? 

Whence results the equality of height at which liquids rise in tubes 
communicating with each other ? 



148 HYDROSTATIC?. 

tabes freely cemmimicating with each other, whatever may be their 
peculiar forms or dimensions ; and this indeed is a necessary con- 
sequence of the common tendency^ of every liquid to act with equal 
force in all directions, producing equality of pressure on the solid 
body or bodies by which it may be encompassed, and extending; 
itself, where unconfined, till every portion of its surface has as- 
sumed a common level. 

76. When two liquids or any greater number, differing from 
each other in specific gravity, are placed in contact, as when in- 
cluded in a glass jar or bottle, unless they are capable of uniting 
to form a chemical compound, it will be perceived that each liquid 
becomes arranged in a separate and distinct stratum, the heaviest, 
or that which has the greatest specific gravity, sinking to the bot- 
tom of the jar, and presenting a level surface above, on which rests 
the next heaviest liquid ; the others in the same manner taking 
their places according to their respective degrees of relative or 
specific gravity. Thus mercury, water, olive-oil, and sulphuric 
ether, might be poured into the same phial, in which they would 
form separate layers, standing one above another, in the order in 
which they have been mentioned ; water being much lighter than 
mercury, oil lighter than water, and ether yet lighter than oil. 

77. Many liquids, differing in specific gravity, may be mixed 
by agitation so as to form a compound ; but if the lighter liquid be 
poured gently on the surface of the heavier, they will for a long 
time remain distinct, but little action taking placf "^sn where the 
surfaces meet. Every body knows that water may be mixed with 
port wine or spirits, both which are lighter than thai, iiquid, as may 
be shown by the following experiments. 

Suppose A B to represent a double-bodied vessel 
the only communication between the upper and 
lower portions of which is through the tube C and 
D ; then if the part B be filled with water to the 
neck, and A with port wine, so as to rise above 
the tube D, still no mixture or alteration in the 
state of the liquids will take place, for the lightest 
occupying the highest situation will retain it un- 
disturbed. But if the lower part be filled with 
port wine, and the upper with water, the former 
fluid will ascend through the tube D, and the latter descend through 
the tube C, till they have entirely changed places. A vessel 
of this construction, having the upper part transparent, and the 
lower part opaque, would form an amusing philosophical toy, by 
means of which might be exhibited an apparent conversion of water 
into wine. An analogous experiment may be made by taking a 

What happens, v. hen two liquids, incapable of chemical union, and of 
different specific gravities, are put into the same vessel ? 

With what liquids might this truth be illustrated ? 

Is the actual mixture of two liquids capable of combining, a certain 
consequence of placing the one upon the other ? 

By what arrangement of apparatus might this be exemplified ? 




SPECIFIC GRAVITY. 



149 



small bottle, with a long narrow neck, not more than the sixth of 
an inch in diameter, which is to be filled with spirit of wine, tinged 
red, by infusing in it raspings of sanders wood, or yellow, by put- 
ting into it a small quantity of saffron ; the bottle thus filled with 
the coloured spirit is then to be placed at the bottom of a deep glass 
jar of water, when the spirit will be seen to ascend like a red or 
yellow thread through the water, till the whole has reached the 
surface. 

78. Bodies, differing in specific gravity, and incapable of com- 
bination, may be shaken together in a phial, and mixed for a time, 
but will separate completely on being allowed to remain at rest. 
Such is the effect exhibited in the following mimic representation 
of the production of the four elements from chaos. A glass tube, 
about an inch in diameter, closed at one end, or a deep phial, being 
nearly filled with equal parts in bulk of coarsely powdered glass, 
oil of tartar, proof spirit, and naphtha, or spirit of turpentine, the 
former spirit tinged blue, and the latter red,* the tube or phial 
must be secured with a cork ; and when it is briskly shaken the 
four imaginary elements will form a confused dull-looking mass, 
but on setting the phial upright, and suffering it to remain undis- 
turbed for some time, an entire separation will take place between 
the several portions of the chaotic mixture : the powdered glass 
at the bottom representing earth ; the oil of tartar, floating above 
it, water ; the spirit, with its cerulean tint, occupying the place of 
air ; and the glowing naphtha at the top designed as an emblem 
of elementary fire. 

79. When two liquids, varying in specific gravi- 
ty, are included in a bent tube, as represented in 
the annexed figure, they will not stand at the same 
height on both sides of the tube, like a single liquid : 
but their respective heights will be in the inverse 
ratio of their specific gravities. Thus, as any given 
bulk of mercury weighs nearly fourteen times as 
much as an equal bulk of water, one inch of mer- 
cury, M, would equipoise about fourteen inches of 
water, W, on the opposite side of the bent tube. 
Neither the form nor the dimensions of the tube are 
of any importance to the result of this experiment; 
for as in other cases of hydrostatic pressure, a small quantity of 
water may be made to counterbalance the larger quantity of the 
heavier fluid mercury, provided the column of water stands per- 
pendicularly fourteen times as high as the column of mercury. 

What happens when two liquids incapable of combination are shaken 
together ? 

Describe the apparatus known by the name of the four elements. 

What occurs where the bent part of an inverted sypon is occupied by 
mercury, and one of the branches is afterwards filled with water ? 

* The blue tint may be communicated to the proof spirit by adding a 
small portion of tincture of litmus ; and the other spirit may be coloured 
with dragon's blood. 

n2 




150 , HYDROSTATICS. 



- 40- - 



■a- 



80. On the principle now stated, a ready method might 
be contrived for ascertaining the relative weights or spe- 
cific gravities of any two liquids, as oil and water, or 
water and ether, or spirit of wine. For this purpose it 
would merely be requisite to procure a glass tube, bent 
and graduated as represented in the margin ; then on 
pouring into the upright branches, equal quantities by 
weight of the respective liquids, their relative weights 
would appear on inspection ; being inversely as the 
h heights to which they would rise in the branches of the 
^~7 tube. The accuracy and utility of such an instrument 
would be augmented by filling the lower portion of the 
tube with mercury, and the graduated branches being of equal 
diameter, given weights of any liquids, which would not act che- 
mically on the mercury, would show, by their respective heights 
on either side, how much greater space an ounce, a dram, or any 
other quantity of one liquid would take up than an equal quantity 
of the other ; and hence it would appear how far the specific gra- 
vity of the latter exceeded that of the former.* 

81. As the specific gravity of a liquid is indicated by the relative 
space which any given portion by weight occupies, so in the same 
manner the specific gravity of a solid body may be inferred from 
the bulk of water or any liquid of known specific gravity, which 
an ounce, a pound, or any similarly ascertained quantity of the 
solid would displace when plunged in the liquid. On this princi- 
ple depend the usual methods of determining the specific gravities 
of bodies, by means of hydrostatic balances, hydrometers, are- 
ometers, and oleometers.f 

82. The discovery of this fundamental principle of science has 
been generally ascribed to the Syracusan philosopher, Archime- 
des, and the circumstances relating to it are thus reported by 
Vitruvius.:}: Hiero, King of Syracuse, having ordered an artist 

How might the principle involved in that experiment be applied to de- 
termine the relative weights of different liquids ? 

What is the relation between the density of a liquid and the space 
which a given weight of it must occupy ? 

How may the specific gravity of a solid be found without reducing it to 
any particular form or bulk ? 

What instruments are employed to determine relative weights of bo- 
dies ? 



* An instrument in which the two open ends of the tube are turned 
downwards and dipped into separate cups of liquids, and to the bent or 
upper part of which an exhausting spring is applied to produce a partial 
vacuum to raise the liquid, is much more convenient in practice. It has 
long been known in France as the " areometre a pompe." A modifica- 
tion by Dr. Hare is called the litrameter. 

fThe former of these instruments is so called from the Greek T£«p, 
water, and m=t P ov, a measure ; and the latter from A e a.<o c , light, or hav- 
ing comparative levity ,'and MsTpov. Oleometers test the value of lamp oil. 

£ Arohiteetur. lib. 9. cRp. 3. 



SPECIFIC GRAVITY. 151 

to make him a golden crown, after it was completed found some 
cause for suspicion that the goldsmith had imposed on him by 
mixing with the gold, with which he had probably been furnished 
from the royal treasury, an inferior kind of metal. The investi- 
gation of this matter was referred to Archimedes, who appears to 
have been unable for some time to contrive any satisfactory method 
of ascertaining whether the crown consisted of mixed metal or 
pure gold. At length, on the occasion of his getting into a bath, 
he observed that the water rose on the sides of the marble basin 
or reservoir in which he stood, in exact proportion to the bulk of 
his body beneath the surface of the fluid. At once the idea flashed 
on his mind that every solid plunged under the surface of water 
must displace precisely an equal bulk of that liquid ; and as 
solids, bulk for bulk, are some lighter than others, the compara- 
tive or relative gravity of two or more solids might be ascertained 
by immersing equal weights of them in water, and observing the 
quantity of liquid displaced by each of the solids. Convinced 
that he could by this means find out whether Hiero's crown had 
been adulterated, the philosopher is said to have leaped from the 
bath, in a fit of scientific ecstasy, which rendered him insensible 
to every thing except the importance of the principle he had dis- 
covered, and running naked through the streets, he exclaimed 
aloud, ^Eypx* — *Eupwa." " I have found it out! — I have found 
it out !" 

83. In order to apply his theory to practice, he procured a mass 
of gold and another of silver, each having just the same weight 
with the crown : then, plunging the three metallic bodies suc- 
cessively into a vessel quite filled with water, and having care- 
fully collected and weighed the quantities of the liquid which had 
been displaced in each case, he ascertained that the crown was, 
bulk for bulk, lighter than gold, and heavier than silver ; and he 
therefore concluded that it had been alloyed with the latter metal. 

84. In comparing the relative or specific gravities of bodies, it 
is necessary that there should be some standard to which the 
respective weights may be 'referred. It might be stated that pla- 
tina is as heavy again as silver, and that cast iron is not much 
more than half as heavy as mercury; but it would not be possible 
from these data to decide whether silver would sink beneath the 
surface of mercury ; for though it is clear that cast iron would 
float on mercury, yet unless some further information were given, 
no comparison could be made between the relative gravities of 
silver and mercury. Supposing, however, it be known that mer- 
cury is thirteen times and a half the weight of water, silver ten 

What historical account is given of the discovery of this method of de- 
termining specific gravities ? 

What process was performed by Archimedes to detect the amount of 
alloy in Hiero's crown? 

What standard is it customary to assume in speaking of the relative 
weights of bodies ? 

What renders any such standard necessary? 






152 HYDROSTATICS. 

times and a half, iron seven times and a half, and platina twenty- 
one times, it will be obvious that the last-mentioned metal would 
sink in mercury, while silver as well as iron would remain sus- 
pended on it. 

85. Tables of the specific gravities of a great multitude of 
bodies have been constructed, showing their relative weights, 
expressed in numbers denoting in what ratio they exceed or fall 
below that of water. The adoption of this fluid as the standard 
of specific gravity is attended with several advantages, which 
have induced philosophers in general to consider its density, 
under certain conditions of temperature and atmospheric pressure, 
as affording a convenient point of comparison to which may be 
referred the densities of other bodies, whether solids, liquids, or 
gases.* The extraordinary power of water to resist compression 
by mere mechanic force, except under such circumstances as can 
rarely take place, \ is one of the advantages it presents ; but in 
the prosecution of experiments of a delicate nature, the pressure 
of the atmosphere must be taken into the account in order to en- 
sure accuracy in the results of our calculations. Alternations of 
temperature, as to heat and cold, also affect the bulk of water so 
considerably as to render it absolutely necessary that any sub- 
stances, whose specific gravity we wish to ascertain by experi- 
mental comparison with that of water, should have the same tem- 
perature with the standard liquid, or that allowance should be 
made for any unavoidable difference of temperature. Purity of 
the watery fluid is likewise, as may be supposed, indispensably 
requisite ; rain-water carefully distilled, and thus freed from all 
foreign impregnation, is therefore to be preferred in the prosecu- 
tion of experimental inquiries. 

86. In the London Philosophical Transactions for 1798, is a 
memoir by Sir George Shuckburgh Evelyn, containing an account 
of numerous and important experiments on the specific gravity of 
water, which have served as the foundation of subsequent re- 
searches. He found that a cubic inch of pure distilled water, the 
barometer standing at 29.74 inches, and Fahrenheit's thermome- 

What advantages belong to the standard actually adopted, beyond what 
are possessed by other substances ? 

What relation has temperature to the method of determining specific 
gravities ? 

What is the weight of a cubic inch of water at mean temperature and 
pressure ? 

* The relative density of gases is sometimes estimated by comparison 
with that of atmospheric air, as the standard : but the ratio of the specific 
gravity of atmospheric air compared with that of water being known, tha 
of the other gases may be deduced from computation, when their several 
relations inpoint of density to atmospheric air have been ascertained; and 
on the contrary the relations of the other gases to atmospheric air, as the 
standard of specific gravity, may be computed from a table of specific 
gravities, including the gases, and referring to water as the common unit 
of density. — See Treatise on Pneumatics. 

t See 10—15 of this article. 



TABLE OF SPECIFIC GRAVITIES. 



153 



ter at 6G degrees, weighed 252,587 grains troy. Now it is a well 
ascertained fact that water attains the utmost degree of density 
just before it freezes, its bulk being relatively less at 40 deg. of 
Fahrenheit or 8 deg. above the freezing point, than at any point 
either higher or lower in the scale.* 

87. The difference of the weight of a cubic inch of distilled 
water at 40 deg. and at 60 deg. is somewhat less than half a grain 
troy, whence it may be made to appear from calculation that a 
cubic foot of pure water, at its greatest density, weighs almost 
exactly 1000 ounces avoirdupois, or 62^ pounds. If, therefore, 
the specific gravity of water be represented by the number 1000, 
each of the numbers in the following table will express the cor- 
responding weights of a cubic foot of the several bodies included 
in it. Thus a cubic foot of pure gold would weigh 19,258 ounces 
avoirdupois, and an equal bulk of cork but 240 ounces. 

88. Specific Gravities of various Solids, Liquids, and Gases, as com- 
pared with Water at 60 Deg. 



Platina, laminated 


22,069 


Sulphate of Barytes, or 


I 4430 


purified . 


19,500 


Ponderous Spar 


Gold, cast . 


19,258 


Oriental Ruby 


4283 


hammered . 


19,361 


Brazilian Ruby . 


3531 


standard, 22 carat 


s 17,486 


Bohemian Garnet 


4188 


Mercury, fluid 


13,568 


Oriental Topaz 


4010 


solid 


13,610 


Brazilian Topaz 


3536 


Lead, cast 


11,352 


Diamond 


3521 


Silver, cast 


10,474 


Natural Magnet . 


4800 


hammered 


10,510 


Fluor Spar 


3181 


Bismuth, cast 


9822 


Parian Marble, white 


2837 


Copper, cast 


8788 


Carrara Marble, white 


2716 


Brass, cast 


. 8395 


Rock Crystal 


2653 


wire 


. 8544 


Flint . _ . 


2594 


Nickel, cast 


7807 


Sulphate of Lime, or \ 


' 2322 


Iron, cast 


7207 


Selenite . 


malleable 


7788 


Sulphate of Soda, or \ 


2200 


Steel, soft 


7833 


Glauber Salt . < 


tempered . 


7816 


Chloride of Sodium, < 


! 2130 


Tin, cast 


7291 


or Common Salt ' 


Zinc, cast 


7190 


Phosphorus 


1770 



At what temperature is water at the greatest density ? 

What is the weight of a cubic foot of water at its greatest density ? 

What would be the weight in ounces of a cubic foot of platina ? 

Would a block of silver sink or swim in a bath of mercury ? why ? 

Would a piece of steel sink or swim in melted copper ? 

What would be the effect of dropping a bar of lead into a pot of melted 
tin ? 

How many times more matter in a cubic foot of saltpetre than in a like 
bulk of water ? 



See Treatise on Pyronomics. 



154 


HYDROSTATICS. 




Nitrate of Potash, 01 < 


2000 


Honey 


1450 


Saltpetre J 


White Wax 


968 


Sulphur, native . 


2033 


Caoutchouc, or Gum ) 


933 


Plumbago, or Black Lead 1860 


Elastic . 5 


Coal 


1270 


Ivory 


1917 


Sulphuric Acid, or Oil < 
of Vitriol . < 


. 1840 


Isinglass 


1111 


Milk, cow's 


1032 


Nitric Acid 


1271 


Butter 


942 


highly con- < 


1583 


Mahogany . 


1063 


centrated . \ 


Lignum Vitae 


1333 


Muriatic Acid, liquid, ] 


1194 


Dutch Box 


1328 


or Spirit of Salt \ 


Ebony 


1177 


Sea- Water 


1030 


Heart of Oak, 60 years ) 
felled . 5 


1170 


Ice 


930 


Alcohol 


797 


White Fir . 


569 


Proof Spirit 


923 


Willow 


585 


Sulphuric Ether 


734 


Sassafras Wood . 


482 


Naphtha 


708 


Poplar 


383 


Linseed Oil 


940 


Cork 


240 


Olive Oil 


915 


Chlorine, formerly called 


I 3.02 


Oil of Turpentine 


870 


Oxymuriatie Gas 


Aniseed . 


986 


Carbonic Acid, or fixed 


I 1.64 


Lavender . 


894 


air ... 


Cloves 


1036 


Oxygen Gas 


1.34 


Camphor 


QQQ 


Azotic, or Nitrogen Gas 


0.98 


Yellow Amber 


1078 


Hydrogen Gas 


0.08 


White Sugar 


1606 


Atmospheric Air . 


1.21 



89. If the specific gravity of water be represented by 1 instead 
of 1000, then that of platina will be 22.069, the last three figures 
being taken as decimals ; the specific gravity of standard gold will 
be 17.486, that of sea-water 1.030, that of olive oil 0.915 ; and so 
on throughout the table, the three right hand figures representing 
decimal parts, except those denoting the specific gravities of the 
gases, the numbers of which must be thus altered to indicate the 
relations of their specific gravities to that of water. 



Water - 


- 1. 


Chlorine 


- 0.00302 


Carbonic Acid 


- 0.00164 


Oxygen Gas - 


- 0.00134 


Nitrogen Gas - 


- 0.00098 



Which would sink most rapidly in water, a piece of flint, or one of na- 
tive sulphur? 

When alcohol and linseed oil are put into the same vessel, which will 
occupy the higher part ? 

Determine the same, with regard to water and honey — oil of turpen- 
tine and cow's milk — proof spirit and naphtha — sulphuric ether and oil 
of lavender. 

When the specific gravity of water is taken as unity, what must we con- 
sider the last three figures of each number in the table ? 



SPECIFIC GRAVITY OF THE HUMAN BODY. 155 

Atmospheric Air - - 0.00121 
Hydrogen Gas - - 0.00008 

90. From the foregoing table it will appear that almost all bo- 
dies will float on the surface of mercury ; gold and platina, and 
their alloys, being the only substances known of higher specific 
gravity than that metalic fluid, except one or two recently disco- 
vered metals of rare occurrence.* Many bodies will float on the 
surfaces of metal while in fusion : and thus earthy and other sub- 
stances found in metallic ores rise in the state of scoriae to the sur- 
face of the melted metal in the process of reduction. The lava 
discharged from volcanos is a very dense fluid, partly metallic ; 
and hence stones of vast bulk and weight are frequently seen 
swimming on its surface while it remains in the liquid state. 

91. Most kinds of wood will float on water, and but few, as fir, 
willow, and poplar, on rectified spirit. The solution of a solid in 
any liquid increases its density : thus sea-water is heavier, bulk 
for bulk, than pure water ; and an egg which will sink in the lat- 
ter will swim in brine. Hence it sometimes happens that a heavy 
laden vessel, after having sailed in safety across the salt sea, sinks 
on entering the mouth of a river ; owing to the inferior specific 
gravity of the fresh water. 

92. The specific gravity of the human body during life is in 
most cases nearly the same with that of river water, and coincides 
more exactly with that of sea-water ; so that there are probably 
but few persons who would not float very near the surface of the 
sea in calm weather. Corpulent people are, bulk for bulk, light- 
er than those of sparer habits ; for the adipose membrane or fat of 
animals is inferior in specific gravity to water ; whilst lean flesh, 
unless the blood and other juices are drained from it, is of higher 
specific gravity than that fluid, and bone is proportionally much 
heavier than the soft parts of the body. Hence it might be infer- 
red that the power of floating on water does not depend entirely 
on the relative specific gravity of the solids and liquids which en- 
ter into the composition of a human body ; and accordingly we 

Which of the gaseous bodies has the greatest specific gravity ? 

How many and which of them are specifically heavier than atmosphe- 
ric air ? 

Which is the lightest of gaseous substances ? 

Why do the impurities of metallic ores rise, when melted, to the sur- 
face of the mass ? 

What is the nature of lava ejected from volcanos ? 

What effect on the specific gravity of any liquid is produced by dis- 
solving in it a portion of any solid ? 

To what maritime occurrence is this fact applicable ? 

What is the relative specific gravity of the human body compared with 
fresh and with salt water respectively ? 

* Iridium, a peculiar metallic substance discovered by Mr. Smithson 
Tennant, in combination with crude platina, has the specific gravity of 
18.6; and Tungsten is a rare and difficultly fusible metal, the specific 
gravity of which is stated to be 17.2. 



156 HI'HROSTATICS. 

find that the body of a person destroyed by drowning, or thrown 
into water immediately after death, will sink far beneath the sur- 
face ; but after several days have elapsed a body thus treated usu- 
ally rises to the level of the water, in consequence of its having 
become specifically lighter than that fluid, from the accumulation 
of gas within the body, produced by incipient putrefaction. It is 
then chiefly owing to the air included in the cavities of the body 
during life, especially that portion contained in the lungs, that a 
man is enabled to float on the surface of a pond or river. 

93. There are, however, some credible accounts extant of per- 
sons whose bodies were so much inferior in specific gravity to 
water, that they could not descend beneath its surface ; not pos- 
sessing that " alacrity in sinking," which may be literally attri- 
buted to most individuals. In 1767, there was a priest residing 
at Naples, named Paulo Moccia, whose extraordinary facility of 
flotation attracted much public attention. This ecclesiastic could 
swim on the sea like a duck ; when he assumed a perpendicular 
position, the water stood on a level with the pit of his stomach ; 
and it is stated that when dragged under the water by one or more 
persons w T ho had dived for that purpose, as soon as he was re- 
leased, his body would rapidly rise to the surface. It appears that 
the weight of this gentleman's body was thirty pounds less than 
that of an equal bulk of water. This peculiarity of conformation 
doubtless depended partly on his being extremely fat, and having 
very small bones; besides which, probably his lungs were capable 
of holding a larger quantity of air than is usual, and there might 
also have been an accumulation of air in the abdomen, arising 
from the disease called tympany, or from some other cause. 

94. Most very corpulent people, who are at the same time 
strong and healthy, would perhaps find on trial that their bodies 
would float on water ; and those who do not happen to be endowed 
with a superabundance of fat might still in almost all cases, with 
a little application, acquire the habit of floating with facility. 
The capability of breathing freely and at regular intervals is es- 
sentially requisite to enable a person to support himself on the 
surface of water. The head, and the upper and lower extremities 
are relatively heavier than the trunk of the human body ; and the 
head especially, from the quantity of bone of which it is com- 
posed, is the heaviest part of the whole mass, yet unless the face 
at least be kept above water respiration cannot be continued. It 
is therefore of the highest importance that all persons should be 

Will a fat or a lean person float with the greater facility 'in water ? 

What will generally occur when a human body is thrown into water ? 

Why does the body of a drowned person rise to the surface after being 
some days in the water ? 

What extraordinary instance of specific lightness in the human body is 
recorded ? 

On what circumstances did it probably depend ? 

What operation is it necessary to perform while attempting to float on 
the surface? 



ATl'I f«F SWI AIMING. 157 

perfectly aware of the precautions necessary for this purpose ; so 
that any one accidentally falling into the water, and being unable 
to swim, may be instructed how to escape a watery grave. 

95. A person suddenly immersed in water, if not absolutely 
deprived of self-possession by fright, should, on coming to the 
surface after the first plunge, endeavour to turn on the back, care- 
fully keeping the hands down, with the palms extended towards 
the bottom of the water, the legs being suffered to sink rather 
lower than the trunk ; the only parts above the surface will then 
be the face and a small portion of the chest : at each inspiration 
more of the head and chest will rise above the water, and perhaps 
those parts will at first be for a moment covered with the aqueous 
fluid at the interval of expiration of the air. Every thing depends 
on making no effort to raise or keep out of water any part except 
the face, and endeavouring to keep the lungs, and consequently 
the chest as much expanded as possible, without using any irre- 
gular exertions in breathing ; and it may be proper to caution per- 
sons thus circumstanced against struggling or screaming, as worse 
than useless ; for in case any one who might yield assistance 
should be within call, it would be best to wait till the first alarm 
had subsided, and then the involuntary bather, conscious of com- 
parative security, might use his voice with due effect, and with- 
out increasing the hazard of his situation. 

96. But an acquaintance with the art of swimming can alone 
give a person perfect confidence of safety when by accident im- 
mersed in water. It is to be lamented that this is not a more 
general accomplishment ; for it is one which must frequently prove 
of great utility ; and it is much to be desired that it should become 
a branch of education at schools for boys, as being of higher im- 
portance than the more fashionable arts of dancing, fencing, or even 
gymnastics. 

97. It may be questioned whether written instructions alone 
would enable any one to acquire a facility in swimming; and ad- 
mitting their utility, it would be inconsistent with the purpose of 
this work to afford them more than a cursory notice. In swim- 
ming, as in floating, the chief object of attention must be to keep 
the face above water, while the limbs are immersed ; but from the 
different position required, it must be apparent that in swimming, 
not the face alone, but nearly the whole head must be sustained 
above the surface. In making a first attempt, the advice of Dr. 
Franklin may be followed, where he directs the learner to walk 
into water till he reaches a place where it stands as high as 
his breast, and dropping into the clear stream an egg ; as soon as 
it has reached the bottom, he is to lean forward, resting on the 

What measures should be adopted when one is suddenly immersed in 
water ? 

What importance ought to he attached to the art of swimming ? 

What is the first step towards the acquisition of that art ? 

How may the learner be made sensible of the buoyant power of the 
water ? 

o 



1 58 HYDROSTATICS. 

water, and endeavour to take up the egg, when he will become 
sensible of the upward pressure or resistance of the fluid ; and rind- 
ing that it is not so easy to sink as might have been previously 
supposed, the young adventurer would acquire confidence in his 
own efforts, the valuable result of experience. 

98. Corks or blown bladders fitted by strings passing - under the 
arms and across the chest, will afford material assistance in sup- 
porting the upper part of the body in a proper position ; but they 
perhaps rather tend to retard than facilitate the progress of the 
learner, by leading him to form a false estimate of the resistance of 
the water; so that as soon as he makes an experiment without the 
corks he finds himself obliged to recommence his task, and study 
it on a different plan which might as well have been adopted at 
first. If, however, corks or bladders should be used, it is highly 
necessary that they should be secured from slipping down to the 
hips, and thus causing the swimmer to fall with the head vertically 
downwards, and incur the most imminent risk of drowning. 

99. As less exertion would be required in the position of float- 
ing than in that of swimming, there would perhaps be some ad 
vantage in acquiring the power of flotation, as above described, 
previously to attempting to swim. This having been effected, the 
learner might, instead of the common expedient of using corks, 
procure a two-inch pine plank, ten or twelve feet long, and placing 
it in the water, lay hold of it with one or both hands and push it 
before him while learning to strike with his legs. But this or any 
other artificial mode of practice, that may be adopted, should be 
laid aside as speedily as possible, as the learner cannot too soon 
make himself acquainted with the full effect of the pressure of 
the fluid in which he is moving, and with his own strength and 
power of action ; and till such knowledge is attained he will make 
but slow progress in the art of swimming. 

100. The method of communicating buoyancy to solids of greater 
specific gravity than water, and enabling them to float in that 
fluid, by inclosing within them air or ga£, is susceptible of appli- 
cation to a variety of useful purposes. It has accordingly been 
adopted in the construction of swimming-girdles, life-preserving 
belts, and air-jackets, which like the bladders noticed above, are 
merely bags of different shapes contrived so as to be inflated with 
air, and worn round the upper part of the body. Life-boats or 
safet} r -boats, as they are sometimes called, are rendered buoyant 
by forming in their sides air-tight cells or lockers, of sufficient di- 
mensions to prevent the boat from sinking even when every other 
part of it is filled with water. It has recently been proposed to 
extend this principle to vessels of any size, and thus to prevent 

What objection exists to the use of cork jackets and similar expedients 
to increase the buoyancy of the body when learning to swim. 

What use may be made of the swimming board while learning the art? 

Explain the construction and use of the girdle employed for the same 
purpose. 

How are life-boats made incapable of sinking? 



CAUSES OF BUOYANCY OF SOLIDS. 159 

heavy laden merchant ships or men of war from foundering- at sea. 
The scheme consists in the employment of copper tubes of a cy- 
lindrical form, hermetically closed at the ends and sufficiently large 
and numerous to contain as much atmospheric air as would cause 
a ship to swim, when in consequence of having sprung a leak it 
would otherwise sink. It is stated by the inventor of these safety 
tubes, Mr. Ralph Watson, that an eighty-gun ship, even when im- 
mersed from leak, would not require the application of such tubes 
to a greater extent of displacement of water than would be suffi- 
cient to support 240 tons of its immense weight. 

101. Fishes, in general, are provided b) r nature with a peculiar 
apparatus, which enables them to swim with the utmost facility, 
and to ascend close to the surface of the water, or descend to a 
considerable depth beneath it, by means of a membranous bag or 
bladder containing air, which they can distend or contract, and 
thus alter their specific gravity according to circumstances. The 
toad fish it is said distends its stomach by swallowing air, to as- 
sist it in swimming, and becomes puffed up like a blown bla.Uef., 
in the same manner as the globe or balloon fish. 

102. An experiment has been previously related exhibiting the 
effect of the pressure of water upward in supporting a plate of 
metal, in contact with the lower extremity of an open cylinder, 
from which it may be inferred that solids of the highest specific 
gravity, as gold or platina, may be made to float on water or any 
other liquid, provided the floating body be of such a form that its 
upper surface may be protected from the pressure of the liquid by 
a column of air, the depth of which bears a certain proportion to 
the specific gravity of the solid. It is thus that a china tea-cup," 
though much heavier than an equal bulk of water, will yet float 
on that liquid if placed in it with its cavity upwards and empty ; 
but on pouring water into it, the cup will descend in consequence 
of the air within its cavity being displaced by the heavier fluid ; 
till at length, when so much water has been poured in as to ren- 
der the cup and water together heavier than a quantity of water 
equal to the space the cup occupies when immersed to its edge, 
it will sink to the bottom. 

103. A raft will float, because it is absolutely lighter than water, 
and a life-boat also for the same reason ; but vessels in general, 
from the cock-boat to the largest man of war, owe their buoyancy 
to their concave form. Hence ships need not be built of fir or any 
light wood, since not only the heaviest woods might be used but 

How are Watson's safety tubes to be applied for the security of vessels 
at sea ? 

To what is the power of vertical movement in fishes attributable ? 

How may the heaviest of metals be made to float on the lightest of li 
quids ? 

What quantity of water will it be necessary to pour into a floating ba 
sin in order to sink it to the water's edge ? 

How is the floating of a raft to be explained ? 



1 60 HYDROSTATICS. 

even the heaviest metals, to construct floating vessels ; and indeed 
steam boats made of sheet iron have recently been tried, and found 
to possess the requisite properties for ploughing the waves with 
perfect facility and safety. 

104. Floating bodies may be employed to raise heavy substan- 
ces from the bottom of a river, pond, or basin of water. Thus a 
sufficient number of air-tight casks might be attached by ropes or 
chains to a large block of granite at the bottom of a river near its 
entrance into the sea, and the ropes being adjusted to such a length 
as to keep them strained tightly by the buoyancy of the casks at 
the lowest ebb of the tide, the block would be raised by the up- 
ward pressure of the casks at high water. Perhaps this method 
of raising or lowering ponderous masses of stone might be advan- 
tageously applied to practice in building bridges or piers within 
the tide-way of a river. 

105. The common method of regulating the supply of water 
conveyed by pipes into a cistern by means of what is called a ball- 
cock, depends on the action of a hollow globe of such dimensions 
relatively to the thickness of the metal as to keep it always float- 
ing on the top of the water in the cistern. A long wire is con- 
nected with the ball at one end, and at the other with a valve or 
stop-cock, on which it acts as a lever, opening it when the long 
arm of the lever is allowed to descend by the sinking of the ball 
attached to that end, when the water falls in the cistern, and on 
the contrary closing the valve, when, by the rising of the ball with 
the water, the cistern becomes full, and the lever presses on the 
valve or cock and keeps it shut, so that the cistern can never be 
filled beyond the proper height. 

106. The power of floating bodies may also be applied in a dif- 
ferent manner to the purpose of rendering buoyant other bodies 
attached to them ; and among the various applications of this prin- 
ciple may be noticed the ingenious invention called the water-camel, 
used in Holland and also in Russia and at Venice, to enable large 
and heavy laden ships to pass shoals or sand-banks. The method 
of effecting this object consists of the application of two long 
narrow vessels adapted to the sides of the ship, and being hollow 
and water-tight they are filled with water, and then let down, and 
firmly secured on each side of the ship, after which the water is 
to be pumped out of them, and the whole mass, consisting of the 
ship and camel is thus rendered specifically lighter than before, 
and drawing less water than the ship alone did previously, 
the shoal or sand bank may be passed without danger of ground- 
ing. 

How does it differ from that of an iron steamboat! 1 

To what useful purpose may the principle of floatation be applied in 
connexion with submarine operations ? 

In what manner is the same principle applied to regulate the access of 
water to a cistern ? 

Explain the construction and use of the water-camel ? 



CENTRE OF BUOYANCY. 161 

107. The tendency of a floating- body to assume a particular 
position when partly immersed in a liquid, and to retain or lose 
that position according to circumstances, may be elucidated by 
reference to the doctrine of the centre of gravity, as explained 
with relation to solids.* When a solid body, specifically lighter 
than water, is placed on its surface, it will sink to a certain depth 
at which the absolute weight of the body is exactly counter- 
balanced by the upward pressure of the water. The point at 
which the entire weight of a body acts with greatest effect must 
be its centre of gravity ; and that point at which the sustaining 
efforts of the liquid are most effective may be termed the centre 
of buoyancy, which must evidently coincide with the centre of 
gravity of the portion of water displaced by the floating body ; and 
if the body be of uniform structure with the centre of gravity of 
that part of it which is under water. A floating body cannot 
maintain itself in a state of equilibrium, unless its centre of gra- 
vity be situated in a vertical line over its centre of buoyancy, or 
immediately under that point. In the former case it will be in 
the state of instable equilibrium, and in the latter in that of stable 
equilibrium. f 

108. Hence the necessity of placing iron bars, stones, or other 
heavy substances in the hold of a ship by way of ballast when it is 
not freighted, or is laden with very light merchandize, in order that 
its centre of gravity may not be elevated too much above its centre 
of buoyancy. It is not requisite that the centre of gravity should 
be reduced below the centre of buoyancy, for though such a dispo- 
sition would contribute to the stability of the vessel, the resist- 
ance to its passage through the waves would be so great as to 
make it sail heavily. In determining the proper situation of those 
points regard must be had to the shape and dimensions of a ves- 
sel as well as to the nature of the cargo or lading, and the manner 
of stowing it ; and on a due attention to these circumstances its 
security and rate of sailing must in a great measure depend. 

109. The methods adopted for ascertaining the specific gravities 
of bodies are founded on the relation between bulk or dimension, 
and weight, which may be determined by various operations, 
according to the nature of the several substances, whether solid, 
liquid, or gaseous, to which they are applied. The relative den- 

What takes place in regard to the centre of gravity of a floating body ? 

How deep will such a body when specifically lighter than water always 
sink in the liquid ? 

What name is given to the point at which the whole buoyancy of the li- 
quid may be conceived to be concentrated ? 

What will be the relative position of the centre of gravity and of the 
centre of buoyancy of a body floating at rest on the surface of water? 

Why are heavy articles stowed in the hold rather than on the deck of a 
vessel ? 

* See Mechanics, Nos. 125— 133. f Ibid. 137—141. 

o 2 



162 HYDROSTATICS. 

sity of different solids may be discovered 03^ simply weighing a 
cubic inch of each ; but unless the process of measurement and 
that of weighing- are both executed with scrupulous accuracy the 
result must be uncertain, and the former of these operations at 
least, must, in many cases, be difficult, and in some impracticable. 
Hence the method adopted by Archimedes is to be preferred, and 
it may be improved by merely weighing the subject of the experi- 
ment first in air and then in water, and noting the loss of weight 
that takes place in the latter case, as that must be equal to the 
weight of the water displaced by the substance under examina- 
tion. 

110. On this principle is constructed the hydrostatic balance, 
which may be used to determine the specific gravity of liquids, 
as well as that of solids. For this purpose a globular or egg- 
shaped mass of glass or crystal must be suspended by a hair or 
fine silk thread from a hook at the bottom of one of the scales of 
an accurate balance, and its weight is then to be ascertained first 

.in the air, next in distilled water, and lastly in the fluid whose 
specific gravity is required ; then by deducting the loss of weight 
of the glass in water from the loss observed when it was weighed 
in the liquid, "the specific gravity of the latter, with reference to 
that of water, will be obtained. By using a glass globe of such 
dimensions as to lose 1000 grains in water, its loss of weight in 
any liquid would at once indicate the specific gravity of that 
liquid. 

111. Insoluble solids denser than water are easily subjected to 
experiment; but any insoluble solid body, which is specifically 
lighter than water, requires, in order that its specific gravity 
should be ascertained, the addition of some heavier substance, so 
that the joint mass maybe made to sink in water; then its weight 
in air and in that liquid respectively being determined, the specific 
gravity of the lighter solid will be the difference between the 
weight of the heavier body in water alone, and that of the joint 
mass, deducted from the difference of their weight in air. Solid 
substances, soluble in water, such as salts, may have their spe- 
cific gravity ascertained by weighing them in alcohol, or some 
other liquid which will not dissolve them, and their specific gra- 
vity, water, being the standard, may be found by computation ; 
or they may be weighed in water after being defended from its 
action by coating them thinly with melted bees-wax. 

What are some of the methods of determining the specific gravity of 
bodies ? 

What is the construction of the hydrostatic balance, and how is it ap- 
plied to this purpose ? 

What method is it necessary to adopt in ascertaining the specific gravity 
of solids lighter than water ? 

How can we take the specific gravity of solid bodies which are soluble 
in water? 



CAPILLARY ATTRACTION. 



163 




112. The most usual and convenient method of 
ascertaining the specific gravities of liquids is by 
means of a hydrometer. This instrument, as re- 
presented in the margin, consists of a hollow glass 
ball B, with a smaller ball of metal C, appended 
to it, and which, from its superior weight, serves 
to keep the instrument in a vertical position, to 
whatever depth it may be immersed in a liquid. 
From the large ball rises a cylindrical stem A D, 
on which are marked divisions into equal parts ; 
and the depth to which the stem will sink in water, 
or any other liquid fixed on as the standard of spe- 
cific gravity being known, the depth to which it 
sinks in a liquid whose specific gravity is required 
Avill indicate, by the scale, how much greater or 
less it is than that of the standard liquid. 



Capillary Attraction. 

113. Liquids are distinguished by the property of preserving 
a level surface when at rest, and rising to the same height in any 
number or variety of communicating tubes ; an effect resulting 
from the joint action of the cohesion of their particles and the in- 
fluence of universal gravitation. But there are certain circum- 
stances in which liquids may be placed, in consequence of which 
the phenomena will be remarkably modified, and a portion of a 
liquid mass may rise far above the common level, and preserve its 
elevation, as if exempt from the power of gravity. Water may 
be made to rise perpendicularly to a great height in an exhausted 
tube ; and even mercury, one of the heaviest of fluids, may be 
seen to be elevated in the same manner in a barometer tube 29 
or 30 inches above the level of the liquid in the basin, into which 
the open end. of the tube is plunged. But in these cases, as we 
shall subsequently show, the influence of gravitation is distinctly 
perceptible, and the liquids rise in exhausted tubes, in consequence 
of pneumatic pressure.* 

114. There is, however, another case in which liquids rise above 
their common surface level, not being inclosed in exhausted tubes, 
but in tubes open at both ends, or between solid plates nearly in 
contact. This phenomenon is styled Capillarity, and is said to be 
caused by Capillary Attraction. f Instances of the operation of 

How are the specific gravities of liquid substances commonly ascer- 
tained ? 

Explain tUe construction of the hydrometer ? 

In what manner may water be made to rise above the general level of 
its mass ? 

Is the exhaustion of tubes in all cases necessary to produce that effect } 

To what phenomenon is the term capillarity applied ? 

* See an account of the Barometer, in Treatise on Pneumatics. 
+ From capillns, a halt*, or capillaris, hair-like, in reference to the 
small bore of tubes which produce these effects. 



nu 



HYDROSTATICS. 



this principle are constantly taking- place around us, and thougn 
highly interesting, they are overlooked by common observers. 
If a slice of stale bread an inch square, and three or four in 
length, be held perpendicularly with one end immersed in a small 
quantity of water or milk, the liquid will ascend through the pores 
of the bread till it is entirely absorbed, and if there is a sufficient 
quantity of it, the bread will become saturated with the moisture. 
In the same manner water or any aqueous fluid will ascend and 
spread through a lump of sugar or a heap of sand, if the base of 
either be immersed in the liquid. 

115. Tubes of glass having a very small bore, and therefore 
called capillary or hair-like, if dipped a little way beneath the sur- 

yface of water, will cause the liquid to ascend to a height bearing 
n. a certain relation to the diameter of the tube. If that diameter 
be 1-50 of an inch, water will rise to 2i inches ; if it be but 1-100 
of an inch, it will rise 5 inches ; and so on in the inverse ratio 
of the diameter of the tube. Similar effects may be exhibited by 
means of two plates of glass, placed as represented in the margin 
in a shallow vessel of water, so that their edges on one side, A C, 
may be in contact, and the other 
B D and E F, somewhat separated. 
The liquid will then rise between 
the plates, standing highest on 
that side where they most nearly 
approach, and gradually declining 
towards the sides that are separated, 
the upper surface of the elevated 
portion of the fluid forming the 
curve F G H, the height of the li- 
quid at any point, as H, being great- 
er in proportion, as it is nearer to the side of the plates A C. 

116. It is in consequence of capillary attraction that a sponge 
imbibes water, blotting paper absorbs ink, or that oil arises amidst 
the fibres of the cotton-wick of a lamp. These effects are mani- 
festly owing to a common cause, and we learn from experiment 
that it is only under certain conditions that they take place. Thus, 
all liquids will not rise to the same height in the same tube, for 
water will rise higher in a capillary glass tube than alcohol, and 
neither of these liquids will rise at all in the finest metallic pipe, 
nor in a glass tube, if the inside of it be greasy. Mercury, on the 
contrary, will not rise in a clean glass tube, especially if it be 
wetted ; while it becomes elevated, when the inside is lined with 
a very thin film of bees-wax or tallow. 

117. Some remarks have been elsewhere introduced, relative to 




From what exhibition of the principle is its name derived ? 

How may the progressive increase of capillary attraction be experi- 
mentally exhibited ? 

Is the same amount of capillary attraction exhibited by a solid towards 
all sorts of liquids ? 



CAPILLARY ATTRACTIOX. 165 

the effect of cohesive attraction on the particles of liquids, caus- 
ing them to assume a globular figure, and on the modifications 
produced by the attraction of solids with which the liquids may 
come in contact.* It is on the joint operation of these causes 
under particular circumstances that the phenomena of capillarity 
appear to depend. It is found from observation that when fluids 
rise in capillary tubes, the surfaces are concave or depressed in 
the centre ; and on the contrary, when the fluids do not rise, they 
have convex surfaces, or stand highest in the middle. These ef- 
fects are manifestly owing, in the first case, to the superiority of 
the attraction between the liquid and the tube over that between 
the particles of the former ; and in the second case, to the in- 
feriority of the former attraction compared with the latter. Hence 
also if water be poured into a glass tumbler it will rise somewhat 
at the edges, while mercury poured into the same vessel would 
be depressed at the edges."}" 

On what causes do the phenomena of capillary attraction depend ? 
What surfaces do liquids in tuhes ordinarily present ? 
What causes the diversity in this case ? 

* See No. 5 of this treatise. 

t See Journal of the Franklin Institute, vol. xiv. p. 147, for some inge- 
nious experiments on capillary attraction, hy Mr. J. W. Draper.— Ed 



The following, among other treatises, may be profitably con- 
sulted in regard to this branch of philosophy, and will generally, 
perhaps, be attainable without much difficulty by the American 
teacher. 

Cambridge Mechanics, by Prof. Farrar, p. 289 — 368. 
Fischer's Elements, p. 83 — 111. 

Playfair's Outlines of Natural Philosophy, vol. i. p. 168 — 193. 
Gregory's Mechanics for Practical' Men, Philad. edit. p. 284 — 
301. 

Library of Useful Knowledge — Treatise on Hydrostatics. 

Robinson's Mechanical Philosophy, vol. ii. 

Edinburgh Encyclopedia, article Hydrodynamics. 

Hydrodynamique, Bossut. 

Hydrodynamique, Prony. 

Traite de Physique, par Biot, vol.i. chap. 22. 

Mecanique Celeste, translated by Bowditch, book 10. 



HYDRAULICS. 

1 When the equilibrium arising from the weight and conse- 
queni pressure of liquids is disturbed, motion will take place ; and 
the laws by which it is regulated are the same with those which 
govern the motion of solid bodies. The velocity of flowing water, 
like that of falling bodies, depends on gravitative attraction, and 
is to be estimated on the same principles ; and the phenomena 
exhibited by jets of water, or other spouting liquids, are analo- 
gous to those displayed by solids projected through the air, the 
effects in both cases depending on the operation of similar causes. 

•2. Among the circumstances which influence the motions of 
liquids, one of the most important is the weight -of the air, pro- 
ducing atmospheric pressure ; and to this force the most powerful 
and useful machines for raising water chiefly owe their efficiency. 
Such are the various kinds of pumps, fire-engines, and siphons, 
which are rather to be considered as pneumatic than as hydraulic 
machines, resembling in their mode of action the barometer and 
the common syringe ; their construction and effects may there- 
fore be most advantageously investigated and explained in treat- 
ing of pneumatics. Indeed that branch of hydrostatical science, 
which relates to the motion of liquids, is so intimately connected 
with the theory of motion, as applicable to all fluids, whether 
liquid or gaseous, that in a systematic treatise the subjects could 
not with propriety be separated. 

3. At present, we shall confine our attention to the effects of 
the motion of liquids on different parts of connected masses, or 
on solids with which they may come in contact ; and afterwards 
briefly notice the construction and mode of action of those ma- 
chines whose power depends on the weight or pressure of flowing 
liquids, or on the pressure or impact of liquids on solid bodies. 

4. In consequence of the imperfect cohesion of their constituent 
particles, liquids present some peculiar appearances, when they 
fall through the influence of gravitation. A continuous solid mass 
will always remain at rest While its centre of gravity is supported ; 
thus it may be sustained by net-work, or suspended by a line, as 
securely and steadily as if it were inclosed on all sides ; but an 
unconnected mass, as a heap of sand, can have no common centre 
of gravity, and therefore to preserve its stability every separate 
grain must be supported. Water, or any similar liquid, in order 
to keep it in the state of equilibrium, requires support even to a 
greater extent than a disintegrated solid, or powder ; for such is 
the peculiar attraction existing between the particles of a liquid, 

What laws regulate the motions of liquids ? 
On what does the velocity of flowing water depend ? 
What circumstance modifies the motions of liquids? 
Under what two general divisions may liquid motions he examined ? 
What peculiarity is presented by liquids when falling in obedience to 
gravitation ? 

106 



FORCE OF FLOWING WATER. 167 

that unless Ihe whole mass be supported laterally as \re J as at 
the base, it will spread on that side where the pressure is with- 
drawn till every part has attained a common level. This property, 
and its effects in producing; pressure in liquids at rest, have been 
already noticed, and those which are exhibited by flowing liquids 
are now to be developed. 

5. When water contained in a deep vessel is suffered to escape 
from an aperture in the bottom, it flows in a continued stream, 
formed by the pressure of the liquid acting against that point from 
which the support has been withdrawn. The combined effect of 
the hydrostatic pressure, and the cohesion of the particles of the 
watery fluid causes various movements in the flowing stream, 
which ma)'- be accurately observed by using a glass jar, and mix- 
ing with the water some very small pieces of amber, or sealing- 
wax, the specific gravity of which exceeding that of water but in 
a trifling degree, they will be carried down with the current, and 
exhibit its internal motions. 

6. The annexed figure will serve to show the man- 
ner in which the liquid descends, at first in horizontal 
strata, and afterwards, when a portion has escaped, 
the surface becomes depressed in the centre, till 
at length, when it approaches the bottom, it as- 
sumes the form of a funnel, or hollow inverted 
cone, which it retains till the vessel is nearly 
emptied. If the aperture be made in the side of 
the vessel, and close to the bottom, the same ap- 
pearances may be observed, with the exception of 
the hollow cone, which in this case does not occur, the liquid re- 
maining level at the surface till it sinks down to the orifice. As 
the common direction of the particles of the descending liquid is 
towards a central point, indicated by the course which the floating 
fragments of sealingwax take towards the aperture, the stream must 
become compressed, and consequently somewhat contracted at that 
point. Its situation depends much on the size of the aperture ; 
and when that is very small, and the side of the vessel in which 
it is pierced extremely thin, the greatest contraction of the jet 
will take place at the distance of about half the diameter of the 
orifice beyond it; and at that point the diameter of the liquid vein 
will be to the diameter of the orifice nearly in the proportion of 5 
to 8, whatever be the height of the liquid in the vessel from which 
it flows. This contraction of the liquid vein may be equally ob- 
served when the discharge takes place from an aperture in the 
side of a vessel, and likewise when the liquid is projected verti- 
cally upwards, as in jets-d'eau. 

What force projects and maintains the continued stream of water How- 
ing from a deep vessel ? 

How may the interior motions in such a vessel he rendered apparent ? 

What appearance on the exterior of an orifice results from the inter- 
ference of the particles of liquid seeking the outlet ? 

Within what limits does the contracted vein approach the diameter of 
the orifice ? 




168 HYDRAULICS. 

7. The point of greatest contraction in a stream of flowing 
water, or of any other liquid, must manifestly be also the point 
whore it has the greatest velocity, as it is there that the hydro- 
static pressure acts with greatest effect. In estimating the velo- 
city of a liquid issuing from an aperture in the side or the bottom 
of any vessel, it will he found to depend on the vertical height of 
the water within the vessel ; and in ever} r case it will he equal to 
the velocity that a body w T ould acquire in falling through a space 
equal to that height. Hence it cannot be unifor n unless the 
water is supplied as fast as it is discharged, and thus kept always 
at the same level. 

8. Suppose two vessels, one of which is 5 inches in height, and 
the other 20 inches, to be filled with water, each having a circu- 
lar orifice at the bottoml-5 of an inch in diameter, if both be open- 
ed, and the vessel kept constantly full by a supply of water above, 
the taller vessel will discharge about 21 ounces of water in a 
quarter of a minute, and the shorter vessel about 11 ounces in 
the same space of time. Thus, estimating the relative velocity of 
the stream in the two vessels by the quantities discharged by each 
in a given time, that of the stream from the taller vessel w T ill be 
to that from the shorter, as 2 to 1, nearly ; and the velocities would 
be exactty in that ratio, but for the effect of friction between the 
particles of the liquid and the sides of the vessel, and the resist- 
ance of the air, which proportionally diminish the discharge from 
the taller vessel somewhat more than that from the shorter one. 
Now taking the velocities as 2 to 1, the height of the taller vessel 
being to that of the shorter as 4 to 1, it will appear that the velo- 
city in either case is as the square root of the height of the column 
of liquid in the respective vessels ; for 1 x 1 = li and 2x2 == -1. 

9. It may, therefore, be general^ stated, that independentl}' - of 
the irregularities occasioned by friction and other causes, the 
maximum velocity with which a liquid fiow r s from an aperture in 
the side or bottom of a vessel will be as the square root of the 
depth of the vertical column within the vessel. Hence the velo- 
city of a flowing liquid depending, like that of a falling body, on 
gravitation, it follows that a stream issuing four feet below the 

, surface of a liquid mass will have double the velocity of one issu- 
ing at 1 foot below the surface; at the depth of nine feet the velo- 
city will be treble, at 16 feet fourfold, at 25 feet fivefold, and so 
on in proportion to the depth of the aperture below the surface. 
It must be recollected that these comparative estimates are to be 
regarded as results deduced from the influence of gravitation 
alone, therefore in practice allowance must be made for the effect 
of friction and atmospheric resistance, and the dimensions and 
form of the aperture must likewise be attended to in making expe- 
riments and calculations. 

In what part of a jet will the greatest velocity necessarily be found ? 
Oa what circumstance does the velocity of issuing- currents depend ? 
Why does not the rapidity of flowing liquids correspond exactly with 
the square roots of the heights, or heads of pressure ? 



/ 



SPOUTING LIQUIDS. 



160 



10. From the experiments of Bossut it appears that the actual 
quantity of water discharged from orifices of the same dimensions, 
under different degrees of pressure, is far less than might be in- 
ferred from calculation. The following table* of theoretical and 
practical discharges through circular orifices one inch in diameter 
will clearly exemplify this principle. 

Height of the liquid Computed discharge per Actual discharge Per 

above the orifice. minute, in cubic inches. per minute. ct. 

1 foot - - 4427 - - 2812 - 63,5 

5 feet - - 10123 - - 6277 - 62,0 

10 feet - - 14317 - - 8860 - 61,8 

15 feet - - 17533 - - 10821 - 61,1 

11. The phenomena exhibited by spouting liquids when the 
current is directed vertically upwards, are equally with those of 
descending currents under the influence of gravitation; and as 
bodies projected perpendicularly in the air rise to a height equal to 
that from which they must have descended, to acquire the velocity 
with which they were propelled,! so liquids spouting from a short 
pipe directed upwards, rise to a height equal to that of the liquid 
column by the pressure of which they were ejected. In the mar- 
ginal figure let A represent a cistern filled with water at the con-V 

stant height B C, then if four bent pipes 
D, E, F, G, be inserted at different dis- 
tances below the surface, the jets will 
all rise to nearly the same level, that of 
the line B C. The resistance of the 
atmosphere and the mutual friction be- 
tween the particles of the ascending 
current, both, however, counteract its 
force, so that it is only when the orifices 
of the pipes are extremely small that 
the elevation of the jets becomes con- 
siderable relatively to the hydrostatic pressure. Yet water may 
be made to rise in spouting streams even above the level of the 
reservoir from which it issues, by introducing a current of air k 
such a manner that it may be mingled with the stream, and tne 
fluid thus becoming specifically lighter than the water in the re- 
servoir, the latter is more powerfully acted on by the incumbent 
weight. 

What do the experiments of Bossut prove in regard to the discharge 
of water from orifices under different heads ? 

Does the difference between the theoretical and the actual discharge 
increase or diminish by an increase of head ? 

What relation exists between the head of pressure and the height to 
which a liquid will be projected upwards ? 

In what manner may a liquid be made to rise in a jet above the level 
of the source ? 




* See Encyclop. Metropol. — Mixed Sciences, vol. i. p. 210. 
f See treatise on JWechanics, No. 91. 
P 




170 HYDRAULICS. 

12. The concourse of the aerial and aqueous fluids produces 
musical sounds, somewhat resembling those from the harmonica, 
but not so soft. That the sounds are caused by the particles of 
the air striking against those of the water is evident, because, 
when the flux of the water is stopped, and the air suffered to issue 
alone, nothing is heard but a hissing noise very different from the 
preceding.* 

13. It has been ascertained from experi- 
ment that a greater quantity of water will be 
discharged in a given time from the side or 
bottom of a vessel, through a short projecting 
tube, than from a simple aperture of the same 
dimensions. The tube, however, must be 
i entirely without the vessel, as in fig. B, for 
C D I if it is continued inside, as at A, the discharge 

V ) will be lessened instead of being augmented. 
y \ ) \ Much also depends on the figure of the tube 

and that of the bottom of the vessel,- since 
more water will flow in the same time through a conical or bell- 
shaped tube than through a cylindrical one, and a further advan- 
tage will be gained by giving a corresponding shape to the bottom 
of the vessel, as at D. These effects depend on the interruption 
to the conflux of the aqueous particles by the sides of the rising 
tube in the vessel A, and the greater facilities afforded for their 
escape in different degrees by the forms of tire apertures in the 
vessels B, C, and D ; and the last of these, coinciding most ex- 
actly with the figure of the flowing stream, is best adapted to pro- 
mote the discharge of the liquid. 

14. When pipes, or tubes, of considerable length are used to 
conduct water from a fountain, the effects will be modified by va- 
rious circumstances, the quantity discharged depending on the 
length and dimensions of the pipes, their direction or inclination, 
and the number and abruptness of the angular bendings which 
take place in their course. 

15. When a stream of water is propelled through a cistern or 
basin containing water at rest, it will have such an effect on the 
entire mass as to set it in motion, and cause a great part of it to 
mix with the current, and make its escape. Owing to this pro- 
perty of flowing liquids, it is possible to drain a lake or marsh by 
leading a stream descending from a higher level to the border of 
the lake, when it will sweep through the stagnant water, and 

What phenomenon accompanies a jet of mixed air and water issuing 
from a pipe ? 

On what circumstances do the effects of short tubes of adjutage depend ? 

What additional causes of resistance are to he considered in long tubes ? 

What occurs when a stream of water is directed along the surface of 
a basin of the same liquid ? 

To what is this effect attributed ? 

* V. Beudant Traite Elementaire de Physique, 1829, pp. 271, 272. 



FORMATION OF WAVES. 171 

gradually drawing; it into its vortex, carry it off over the opposite 
bank. Venturi, an Italian philosopher and engineer, made use of 
this method to drain a marsh near Modena, by conducting through 
it a rapid descending stream.* This effect is produced by fric- 
tion between the particles of the liquid, and thus the water in 
motion communicates its impulse laterally, till the whole mass is 
affected, and gradually entering the current is carried off. 

16. The friction which takes place between the particles of 
water and those of the air is productive of some curious and in- 
teresting phenomena. To this cause is owing the current of air 
caused by the fall of water from an eminence, of which a remark- 
able instance is adduced by Venturi, in a cataract which rushes 
from the glacier of Roche Melon, on the rock of La Novalese, 
near Mount Cenis. 

17. The agitation of the sea by the wind, and the transforma- 
tion of its surface into a mass of foaming waves and mountain 
billows during a storm, is another important and striking effect 
of the friction of air and water. That the formation of waves 
depends on this cause is convincingly proved by the experiments 
of Dr. Franklin, who ascertained that by pouring oil on the sur- 
face of a pond to the windward, in stormy weather, the ripples 
with which it was covered might be made to subside ; and it 
appears that this method of calming the waves by pouring oil on 
their surface has in some instances been found advantageous at 
sea. From its inferior specific gravity the oil forms a floating 
film, which defends the surface of the water from contact with the 
currents of air, and the friction between the wind and waves is 
vastly diminished, in the same manner as that which takes place 
between solids is by the application of unctuous matter. 

18. The effect of the pressure or impact of flowing liquids on 
solids immersed in them, is, as in other instances of hydraulic 
pressure, greatly influenced by circumstances, and therefore the 
general principles arising from theory must be adopted with con- 
siderable limitations when applied to practice. It must be mani- 
fest that when a flat solid surface is moved perpendicularly 
against a liquid, the resistance will always be in a certain pro- 
portion to the extent of the solid surface ; and when such a plane 
surface is exposed to the action of a flowing liquid, the effect must 
be greater or less according to the degree of the velocity of the 
stream. Hence may be deduced the general rule, that the effect 
produced by the pressure of flowing water, acting perpendicu- 
larly on a flat surface plunged beneath it, is in the compound 

To what useful purpose has this experiment been converted ? 
How is the elevation of waves to be explained ? 

What experiment is conceived to demonstrate the correctness of this 
explanation ? 

In what proportions are solids resisted when moving through liquids ? 

* See Leslie's Elements of Nat. Philosophy, vol. i. pp. 397, 398 ; and 
Nicholson's Journal, 4to. 1798. 



1 72 HYDRAULICS. 

ratio of the square of the velocity of the stream and that of the 
solid surface. If the surface be presented obliquely to the direc- 
tion of the stream, the effect must be less than when it is perpen- 
dicular to the surface of the current; and the diminution of pres- 
sure arising from such a cause will be proportioned to the incli- 
nation of the solid surface. Its amount in any given case may 
be calculated on the same principles as the effects of inclined 
planes in mechanics. 

19. When a liquid acts by impact on a solid plane, causing it 
to turn round an axis, in the manner of the float-boards of a water- 
wheel, there will be a certain point in that plane, where, if the 
whole force of the stream could be concentrated, it would produce 
the same effect as when that force is distributed over the whole 
surface of the plane. The point thus indicated is the centre of 
percussion, some notices of which have been introduced else- 
where.* 

Hydraulic Machines. 

20. The object of hydraulic machinery is chiefly that of raising 
water from a lower to a higher level, which effect may be pro- 
duced by hydrostatic pressure or impact, on liquids and solids, 
either alone, or in conjunction with atmospheric pressure. The 
construction of those machines whose operation depends on the 
latter cause must be referred to the treatise on Pneumatics ; but 
there are other machines which may be properly noticed at pre- 
sent as their modes of action admit of satisfactory explanation 
on the principles of hydrostatic science. 

21. These may be distinguished into three classes : namely, 
machines for raising water by mechanical means only ; those 
which act by the weight, pressure, or impact of water, on solids ; 
and those in which the effect is produced by the reactive force or 
intermitting action of flowing water. 

22. A common draw-well, from which the water is lifted by 
means of a bucket and windlass, affords an example of a machine 
of the first class. But the comparatively small quantity of water 
that can be raised at once by the use of a single bucket confines 
its employment to domestic or occasional purposes. 

23. The chain-pump is a much more efficient engine, though 
very similar in its mode of action to the preceding. The figure 

What advantage is possessed by the obliquity of the surface against 
which the resistance is applied ? 

At what point in a float-board may the whole action or reaction of a 
liquid be conceived to be applied ? 

On how many different principles are machines for raising water con- 
structed ? 

Into how many classes are those machines divided, which depend for 
their efficiency entirely on hydrostatic laws? 

* See Mechanics, "N"o. 123. See Col. Beaufoy's experiments on Hy- 
draulic action, in which a vast variety of forms, velocities, and modes of 
action are detailed. — El). 



THE CHAIN-PUMP. 



173 




in the margin represents it as consisting 
of a number of plates or flat disks of 
wood, D D D D, attached horizontally 
to an endless chain, and passing round 
two wheels, E and F, by turning which 
the chain and plates are carried through 
a water-tight cylinder, the lower end of 
which is plunged beneath the surface of 
water, and its internal dimensions are ex- 
actly adapted to receive the plates, which 
successively entering the tube when 
drawn up by the revolving chain, form 
so many buckets filled with water, which 
they carry up and discharge into a cistern 
above, or when used as they commonly 
are on ship-board, into a pipe that may 
discharge it again into the sea. The ma- 
chine may be set in motion by a winch, or other means applied 
to turn the upper wheel. The chain-pump will act with greater 
effect when the cylinder can be placed obliquely than when its 
direction is exactly vertical. 

24. The rope pump is a less efficient modification of the chain- 
pump or bucket-engine. It is composed of wheels, one under 
water and the other above, having on their peripheries several 
grooves, through which pass endless ropes of very loosely spun 
wool or horse hair ; and the upper wheel being made to revolve 
with great velocity, the water which adheres to the coarse ropes 
may be raised and discharged above by pressure. The water is 
here attached to the rope by simple cohesive or capillary attrac- 
tion. 

25. The Persian wheel, which is used to raise water not only 
in Persia but also in Egypt and other eastern countries, consists 
of a large wheel, to the nave of which are suspended a number 
ot buckets, in such a manner that in the revolutions of the wheel 
they successively dip into a pond or stream of water over which 
the wheel moves, and the buckets thus being filled ascend with 
their load till each in ,turn reaches the summit of the circuit, 
where there is a contrivance for tilting each bucket, so that it may 
discharge its contents into a cistern or reservoir, and it then de- 
scends with the revolving wheel to be filled again. Such a wheel 
may be put in motion by any mechanical means ; or if it be em- 
ployed to raise water from a running stream, float-boards may be 
added to make it revolve like an under-shot wheel. 



Explain the action of the chain-pump. 

In what position will the chain-pump act to most advantage ? 
By what species of mechanical action is water raised on a rope pumpr 
Explain the construction of the Persian wheeh 
p 2 



174 



HYDRAULICS. 



jggg^jgggggfc 




26. The cochlion or screw 
of Archimedes, derives its 
designation from a preva- 
lent opinion that it was the 
invention of the Syracusan 
sage. But it is not men- 
tioned by Vitruvius among 
the discoveries of Archi- 
medes, and there is some 
ground for believing that it 
was, before his time, used 
in Egypt to raise and carry off the superfluous water left in the 
]ow grounds after the inundations of the Nile; so that the ques- 
tion as to its origin remains undecided. Its form, as represented 
in the margin, is that of a helix (as the name partly implies,) 
consisting of a flexible tube like a holloAV corkscrew wound round 
a solid cylinder, which may be made to revolve by turning a 
winch, or by attached wheel-work. When it is placed in an ob- 
lique position, with the lower opening of the screw immersed in 
a cistern, or any other body of water, the liquid will enter below, 
as the orifice dips beneath it in each revolution, and be carried up 
and discharged above ; the peculiar form of the machine facilitat- 
ing the elevation of the water. 

27. The most important machines belonging to the second class 
are different modifications of water-wheels. They are respectively 
termed undershot wheels, overshot wheels, and breast wheels. 

The undershot wheel is said to 
be of earlier origin than the others ; 
and it is likewise the most common. 
It consists, as is shown in the an- 
nexed figure, of awheel on the peri- 
phery of which are fixed a number 
of flat boards at equal distances, and 
set at right angles to the plane of the 
wheel. They are called float-boards ; 
and the wheel being so placed as for 
its lowest point to be immersed in 
flowing water, it is set in motion by 
the impact of the water on the boards as they successively dip 
Into it. As a wheel of this kind will revolve in any stream which 
furnishes a current of sufficient power, it may be used where the 
descent of the water is by far too trifling to turn a breast wheel, 
much less an overshot wheel. 

28. If all the float-boards are vertical to the centre of the wheel, 




To whom is the invention of the cochlion commonly ascribed ? 

Into how many classes are vertical water-wheels divided ? 

What name is given to that part of an undershot wheel which receives 
the impact of the water ? 

In what situations is the peculiar advantage of this kind of wheel to be 
obtained ? 



WATER-WHEELS. 



175 



as in the figure, the wheel will work equally well in either direc- 
tion, and one of that construction may therefore be advantageously 
used in the tide-way of a river, as it will revolve either with the 
flowing or the ebbing tide. But in any other situation a wheel is 
to be preferred in which the float-boards incline towards the cur- 
rent, and thus the effect of the stroke is increased ; but it appears 
from experiment that the best position is when the inclination of 
the float-boards is but inconsiderable. 

29. The overshot wheel differs 
from the foregoing in the manner in 
which it is acted on by water, receiv- 
ing its impulse not from the impact 
only, but from the weight of water. 
This kind of wheel, as may be con- 
ceived from the figure in the margin, 
can only be used where a consider- 
able fall of water can be obtained. 
On its periphery are fixed a number 
of cavities called buckets, being 
closed on both sides, but having 
openings, so that the water, conducted by a level trough of the same 
breadth with the wheel, may fill each bucket in succession, as it 
reaches that point in the circuit of the wheel at which the weight 
of the water can begin to act on its circumference. From the pe- 
culiar form of the buckets they retain the water partially till they 
have descended to near the lowest point of the circuit, and having 
discharged their contents into the tail-stream, they ascend on the 
opposite side to be filled as before. As the overshot wheel requires 
the greatest fall of water to make it act, so is it likewise the most 
powerful with reference to the effect produced, by the momentum 




of flowing water. 




30. The breast wheel is a sort 
of machine having an intermediate 
character compared with the un- 
dershot and overshot wheel. It 
has float-boards like the former, 
but they are converted into buckets 
somewhat after the manner of 
those in the chain pump, as they 
move in a cavity adapted to the 
circumference of the wheel, as 
shown in the margin. The water 
passes through this cavity, enter- 



How are the floats of an undershot wheel to be set with respect to the 
centre ? 

Describe the construction and action of nn overshot wheel. 

What relation has the power of the overshot wheel to that of other 
wheels using the same quantity and fall of water ? 

What is the construction of the breast wheel ? 

in what points does it resemble the other two forms of water-wheels ? 



176 



HYDRAULICS. 



ing it nearly on a level with the axis of the wheel. In this case 
the liquid acts chiefly by its weight ; and the machine, though 
less efficient than the overshot wheel, is more so than the other. 
It is, therefore, only used where the fall of water happens to be 
peculiarly adapted for the purpose. 

31. Among the hydraulic machines belonging to the third class, 
which derive their power from the reaction of flowing water, is 
one called Barker's Mill, as having been invented by Dr. Barker, 
towards the close of the seventeenth century. This engine, as 

represented in the annexed figure, consists of a 
hollow cylindrical metal pipe, A B, of consider- 
able height, and terminating above in a funnel- 
shaped cavity. The pipe is supported in a ver- 
tical position, by resting below on a pointed 
steel pivot, turning freely in a brass box, adapt- 
ed to receive it ; and the upper part has a cy- 
lindrical steel axis,C D, passingthroughaboard, 
supported by uprights at the sides. The hollow 
tube, A B, communicates with a cross tube, E F, 
closed at the extremities, but having adjusti- 
ble orifices at the opposite sides, near each end 
of the cross tube. A pipe, G, above, communi- 
cates with a supply of water, which it dis- 
charges into the funnel at the top of the vertical 
pipe B ; and the supply must be so regulated that the pipe may 
be kept constantly filled with water without running over ; while 
the orifices in the cross-pipe at E and F will deliver the water 
with a force proportioned to the height of the column in the tube 
A B, and the apertures being in opposite directions, the spouting 
currents will communicate a rotary motion to the vertical tube and 
its axis C D, to which may be attached a toothed wheel connected 
with any other machinery. 

32. The action of this machine does not, as sometimes stated, 
depend on the resistance of the atmosphere to the jets from the 
cross-pipe ; but is wholly owing to the hydrostatic pressure of the 
column of water in the vertical tube, which exerting great force 
on the interior of the horizontal tube, and that force being removed 
from the points whence the water issues, the pressure or reac- 
tion on the corresponding points on the opposite parts of the in- 
terior of the tube tends to make it revolve, the action of both jets 
producing motion in the same direction. Hence it is often called 
the reaction wheel. The theoretical investigation of its peculiar 
properties and mode of action, has engaged the attention of the 
celebrated mathematicians, Leonard Euler and John Bernoulli, 




By what mechanical property does the water produce its effect on this 
wheel ? 

On what principle is Barker's mill constructed ? 

Is the presence of the air necessary to the action of this machine ? 

On what part of the revolving arms is the moving force really exerted ? 



THE HYDRAULIC RAM. 



177 



both of whom represent it as exhibiting a method of employing 
the force of water as a moving power, superior to any other. 

33. Among machines whose effects depend on the force of flow- 
ing water may be included the Hydraulic Ram, invented, or rather 
improved by Joseph Montgolfier, distinguished for his share in 
in the invention of the air-balloon. The hydraulic ram operates 
chiefly from the momentum of a current of water, suddenly stop- 
ped in its course, and made to act in another direction ; and as it 
produces a kind of intermitting motion, owing to the alternate re- 
treat and access of the stream, accompanied with a noise arising 
from the shock, its action has been compared to the butting of 
rams ; and hence the name of the machine. 

34. Several historical facts, in regard to the employment of the 
percussive force of liquids to elevate portions of their own nass, 
are cited by writers on this subject, prior to the invention of 
Montgolfier's Belier hydraulique. The fixing of pipes to convey 
water from one level to another, could scarcely fail to render ap- 
parent the immense power momentarily exerted when a column 
of water descending with considerable velocity is suddenly arrest- 
ed. A most striking example of this was exhibited (Dec. 1834) 
at the Philadelphia water works, in which, by a little derangement 
in the action of the valves of the force pump, the column of water 
from the basin 100 feet high, was suddenly met by the machine 
with a force which burst the air vessel with an explosion like that 
of artillery, tearing asunder the cast iron at a part where the di- 
ameter of the vessel was three feet, and the thickness of the 
metal full an inch and a half of perfectly sound casting. Several 
inch bolts of wrought iron which had confined the upper part of 
the vessel were likewise torn away. 




35. The essential parts of the hydraulic ram, as exhibited by 
Montgolfier, are represented in the marginal figure. A, is a head 
of water, connected with the tube or tunnel B, closed at the extre- 
mity C, but having an aperture at D, to which is adapted a valve 
formed by a ball of porcelain or copper, hollow, so as to be not 



On what principle is the hydraulic ram constructed ? 
What remarkable effects of the percussion of a liquid column have 
been observed £ 

Explain the several parts of the machine invented by Montgolfier. 



178 HYDRAULICS. 

more than as heavy again as an equal volume of water, and sup- 
ported near the orifice by a sort of muzzle or cage. F, is a reser- 
voir of air, with an opening from the tunnel B, and a valve E fit- 
ted to it, but lifting upward, and prevented from displacement by 
a muzzle over it. From near the bottom of the air-vessel F pro- 
ceeds a pipe G, which may be continued to any given height to 
which it is requisite that the water should be raised. The tube 
B, is called the body of the ram; the tube G, the tube of ascen- 
sion ; D the stoppage valve, and E the ascension valve. 

36. Now the former valve being open and the latter shut when 
the water begins to run, it at first escapes through the stoppage 
valve D, but soon acquiring a momentum, from the accelerating 
velocity of its fall, it drives the ball D against the opening and 
stops the passage in that direction; the reflected stream then 
strikes up the valve E , and water enters into the air-vessel F, 
through the ascension valve : the ball D, as soon as it is relieved 
from pressure, falls into its muzzle, and makes way for the water 
again to escape through the stoppage valve, while the other valve 
closes through its weight and the reaction of the compressed air 
in the reservoir. The renewed momentum of the stream presently 
shuts the stoppage valve, and lifting the ascension valve, more 
water enters the air vessel, and as soon as the orifice of the pipe 
G becomes covered, the pressure of the air drives the water up- 
ward ; for that which has been admitted through the ascension 
valve cannot return, and more being added at each stroke of the 
engine, it may be gradually raised to an indefinite height. 

37. The absolute effect produced must, in any given case, de- 
pend on the fall of water to supply the engine, and the diameter 
and lengths of the tubes. IVtontgolfier erected a water ram in his 
garden, with an artificial fall of water of 7i feet, by which water 
was raised to the height of 50 feet, in tubes two inches in diame- 
ter : the water expended in four minutes was 554 pints, that ele- 
vated 52 pints. Comparing the power expended, (554 X 7.5= 

/ 4155,) with the effect obtained in this case, (52x50=2700,) we 
get the result 2700H-4155=,65, or the effect is sixty-five per cent, 
of the power, while with the best forms of overshot wheels the 
effect sometimes exceeds 85 per cent. In another machine, with 
a fall of about 34 feet, water was raised seven times that height, 
and the stoppage valve closed one hundred and four times in a 
minute. Improvements were made on the original construction 
of the hydraulic ram by the son of the inventor, who obtained, in 
England, a patent for his construction. 

Why does not the stoppage valve remain permanently in contact with 
its seat when once elevated by the force of the current ? 

On what does the absolute effect of the hydraulic ram depend ? 

What proportion did Montgolfier find between the poiver expended 
and the effect produced in the elevation of water ? 



WORKS ON HYDRAULICS. 179 

The subject of hydraulics embraces two different objects.— 
The first, a theoretical view of the nature of the forces exerted by 
water in motion, and the peculiar phenomena accompanying- its 
movement, whether in open channels, closed pipes, or the organs 
intended to receive and employ its mechanical efficiency ; and the 
second regards it as a branch of engineering - . Teachers will find 
the two departments often blended together, and the topics be- 
longing to both promiscuously treated. But in some recent pub- 
lications they have been very properly distinguished, and the 
science of the matter, with its various theoretical developements, 
arranged under appropriate heads. In this manual, the object 
of which is to treat chiefly of the sciences, the former class of 
treatises deserves particular mention. 

Theoretical calculations are to be found in Cambridge Mecha- 
nics, pp. 369 — 417. 

Gregory's Mathematics for Practical Men, pp. 302 — 329. 

Treatise of Mechanics, by the same author, 2 vols. 8vo. 1826. 

Venturi's Experimental Inquiry, translated by Nicholson. 

Lectures on Natural Philosophy, by Dr. Young. 

Belidor's Architecture Hydraulique. 

Prony's Nouvelle Architecture Hydraulique. 

Dubuat's Principes d'Hydraulique. 

Traite Elementaire d'Hydrodynamique, par Bossut. 

The volume of the transactions of the British Association at 
Cambridge, contains an able report by Mr. Rennie, on hydrau- 
lics, as a branch of engineering, which has been republished in 
the Journal of the Franklin Institute for January and February, 
1835. 

For an account of experiments on water power the reader may 
consult Smeaton's Reports, Evan's Millwright's Guide, Banks 
on Mills, and Journal of the Franklin Institute, (report of commit- 
tee on water-wheels.) 



PNEUMATICS. 

1. The object of that branch of physical science which has 
neen denominated Pneumatics,* or Aerology, f is to explain and 
illustrate those phenomena which arise from the weight, pressure, 
or motion of common air or other fluids possessing the same gene- 
ral properties. The distinction between liquids and those more 
elastic fluids called air, gas, vapour, or steam, depends in a great 
degree on occasional causes, especially on temperature and pres- 
sure. Those effects which are to be attributed to the operation 
of heat and cold, or diversity of temperature, are on several ac- 
counts of sufficient importance to be made the subject of detached 
investigation, comprehending a review of the relations of heat to 
all natural bodies, whether solids, liquids, or gases ; and tracing 
the general influence of temperature in the production of those pe- 
culiar forms of matter. Therefore, though it will be impossible 
to explain the phenomena of atmospheric pressure, and its effects 
on solids and liquids, without adverting to the influence of tempe- 
rature, a more extended survey of that important subject must be 
referred to the subsequent treatise on that branch of science which 
has been termed, Pyronomics, or the laws of heat. 

2. There are two kinds of aeriform bodies ; namely, those which 
are always in the gaseous state, under common circumstances of 
temperature and pressure, thence named permanent gases or airs ; 
and those which become gases chiefly at high temperature, and 
which therefore may be styled non-permanent gases or vapours. 
Common air, or atmospheric gas, affords an obvious specimen of 
a permanent elastic fluid, and steam or vapour of water of a non- 
permanent elastic fluid. 

3. These different species of gases possess many properties in 
common ; and there is reason to believe that those gases which 
have till recently been regarded as capable of existing only in the 
form of permanently elastic fluids, might be reduced to the liquid 
state by subjecting them to extremely low temperature and very 
powerful pressure. 

4. Mr. Faraday has effected the condensation to the state of a 
liquid of the gas called carbonic acid or fixed air, as well as 
several other gases previously considered as permanently elastic 

What is the object of the science of pneumatics ? 

On what rests the distinction between liquids and gaseous bodies ? 

What imponderable agent is necessarily involved in the phenomena ot 
atmospheric action ? 

How many kinds of aeriform bodies are found in nature ? 

What constitute their distinguishing properties? 

What has Faraday proved in regard to the state of carbonic acid and 
other gaseous bodies ? 



* From the Greek nw«A*»» breath, or air ; or nv-o^^TJxs,-, aerial. 
t From >A>,p, air; and Aeyo's, a discourse, or treatise. 

180 



GENERAL PROPERTIES OF AIR. 181 

fluids, by the combined operation of pressure and low tempera- 
ture.* And Mr. Perkins, whose experiments on the compres- 
sibilit)'' of water have been already described, extended his opera- 
tions to gaseous bodies, and from his statements it appears that 
he succeeded in reducing atmospheric air to the state of a limpid 
liquid, by a pressure equal to the weight of twelve hundred atmos- 
pheres, f Should the observations of those gentlemen be confirm- 
ed and extended to all those now called permanent gases, it will 
be evident that their existence in the liquid or gaseous form de- 
pends entirely on their relations to temperature and pressure, the 
various airs and vapours being all susceptible of condensation un- 
der different circumstances. 

5. Airs and vapours, or permanent and non-permanent elastic 
fluids, however, though they may be considered as forming but 
one class of bodies, yet from the vast diversity of their relations 
to heat, admit of being applied to very different purposes ; and 
hence, in treating of their physical properties, the distinction 
between them must be carefully kept in view. It will, therefore, 
be conducive to perspicuity to notice in this treatise the properties 
of the permanent gases, such as atmospheric air ; leaving the cir- 
cumstances which constitute the discriminating characteristics of 
the non-permanent gases, and especially of steam or the vapour 
of water, to be more fully investigated in the division of this 
work, appropriated to the doctrine of Heat. 

General Properties of Mr. 

6. Common or atmospheric air is an invisible or perfectly trans- 
parent fluid, the ultimate particles of which appear to be destitute 
of cohesion ; and hence air has a disposition not only to sink 
down, and spread out laterally like liquids, when unconfined, but 
it is also equally capable of expansion upwards ; so that any por- 
tion of this fluid will speedily become dissipated and lost, unless 
it be inclosed within a solid air-tight vessel or other receptacle, 
such as a bladder, or retained in an open vessel by the pressure 
of a liquid on its surface. 

7. That air is porous in a very high degree appears from its 
readily yielding to pressure ; but like all material bodies it pos- 
sesses the property of impenetrability, for though a considerable 
bulk of this fluid may be forced into a comparatively small space, 
there must be a limit beyond which the utmost pressure will cease 
to have any effect. The resistance of air to pressure may be 

What effect did Perkins obtain by subjecting air to the pressure of 1200 
atmospheres ? 

To what conclusions are we conducted by these experiments on gaseous 
bodies ? 

What are the most striking sensible properties of atmospheric air ? 

What appears to be the mutual relation of its particles to each other ? 

* See Ahstracts of Papers in Philos. Trans., vol. ii. p. 192. . 
t Idem, p. 290. 

Q 



182 



PNEUMATICS. 



<r 




demonstrated by means of a syringe of any kind with a solid pis- 
ton ; for if the pipe or lower opening- be firmly closed after the 
piston has been drawn up so as to fill the barrel with air, it will 
be found impossible to thrust doAvn the piston again completely 
while the pipe remains obstructed. 

8. Let a tall narrow-mouthed glass jar or bottle be 
half filled with water A, and a funnel C, with a long 
tube, be inserted in the mouth of the bottle, as repre- 
sented in the margin, and firmly secured at D, by luting 
or by passing it through a cork, in such a manner that 
the included air at B cannot escape between the fun- 
nel and the mouth of the bottle. Then water being 
poured into the funnel, little or none of it would pass 
into the bottle ; for if the funnel had a tube several 
feet, or even yards in length, so as to give the advan- 
tage of strong hydrostatic pressure, though in that case 
the air at B would be compressed into somewhat smaller 
space, yet no imaginable force would fill the bottle, 
which of course would burst under a certain degree of pressure. 

9. Another property of air is compressibility, in which it dif- 
fers most essentially from liquids. It has been elsewhere stated 
that water undergoes no apparent diminution of bulk from pres- 
sure unless vast force is applied to it ; and other liquids in dif- 
ferent degrees resist compression, though readily dilated by heat 
and contracted by cold. But airs and gases, though, as we have 
just shown, manifestly endowed with impenetrability, yet display 
a facility of contraction and expansion under the influence of pres- 
sure, which is completely independent of temperature. They are, 
however, most powerfully affected by changes of temperature also ; 
their bulk increasing or diminishing with the degree of heat to 
which they are exposed. 

10. That the particles of air can be compressed, or driven by 
external force closer to each other than they were before that force 
was applied, must be apparent from the experiments adduced to 
prove the impenetrability of air ; for while those experiments 
show that the particles of the compressed fluid cannot be destroy- 
ed, but will, when exposed to the utmost force, still occupy a cer- 
tain space, yet it appears that contraction always takes place under 
the influence of pressure to a certain extent; and hence may be 
inferred another property of air already noticed , namely its porosity. 

11. The compressibility of air may be experimentally illus- 
trated by means of a strong glass tube closed at one end, like a 
barometer tube, and having fitted to it a piston, consisting of a strong 
iron wire or rod, with moistened leather fixed to one end, so that 
it may move up and down in the tube quite air-tight. Then, the 

How is air proved to possess the property of impenetrability ? 
In what manner is impenetrability manifested in filling a bottle with 
liquid ? 

How do gases differ from liquids in regard to compressibility.'' 
How may the compressibility of air be experimentally illustrated ? 



WEIGHT OF AIR. 183 

tube being full of air, the piston is to be adapted to the open end, 
and if it be cautiously pressed down, the air may be reduced to 
about one-half of its original bulk, without using- much force, and 
by stronger pressure the fluid may be yet further condensed, but 
at length the resistance will be such as to preclude the possibility 
of any greater compression. 

12. The most remarkable among the properties of air is elas- 
ticity, depending on its expansive power, in consequence of which, 
when its dimensions have been reduced by pressure, it immediate- 
ly recovers its bulk on the cessation of the compressing force. 
Thus, if the piston of a common syringe is pushed down while 
the air is prevented from escaping by the pipe, as soon as the pres- 
sure is withdrawn the piston will be raised by the expansion of 
the included air. To this property of air or gas is owing the force 
with which a pellet of wet paper is driven from a school-boy's 
popgun ; and this insignificant little engine acts on the same prin- 
ciple with the air-gun and other philosophical instruments, which 
will be subsequently noticed. 

13. Gravity or weight is another very important property of air, 
which it possesses in common with solids and liquids. Common 
air, as being comparatively lighter than water, will when set free 
below the surface of that liquid, rise through it, in the form of 
transparent bubbles. This is an effect of hydrostatic pressure, in 
consequence of which bodies of inferior specific gravity to water 
when immersed in it are pressed towards its surface ; and thus it 
happens that a cork, a drop of olive oil, or a bubble of air or gas 
will float on the surface of water, and when forcibly pressed be- 
neath it, rise again to the top as soon as the force that kept it 
down ceases to act. 

14. The weight of air may be ascertained in the same manner 
as that of liquids or solids, by the common operation of weighing 
it with a balance. But in consequence of its extreme expansi- 
bility, some peculiar precautions are necessary in performing this 
operation, even when no great nicety is required. These, however, 
will be subsequently noticed; and it will be sufficient at present 
to state that by means of a large bottle with a stop-cock and a 
syringe adapted to it, the weight of a given quantity of air may 
be discovered. For suppose the stop-cock to be left open and the 
bottle weighed in that state, when of course it will be full of air, 
then the weight of the bottle and the included air having been y 
noted, the air must be drawn out, as completely as possible, by ' 
screwing the syringe on to the stop-cock, and working the piston ; 
the stop-cock is then to be turned so as to close the bottle, which 

on being weighed again, after being unscrewed from the syringe, 
will be found to have lost a portion of its weight equal to that of 
the quantity of air which it would hold. 

What effect, resulting from elasticity, follows the compression of ail } 
What familiar facts illustrate this position ? 

What causes the rise of bubbles of air through a mass of liquid ? 
How is the weight of air demonstrated r 



184 PNEUMATICS. 

15. A cubic foot of air weighs about 523 grains ; and conse- 
quently a cubic inch will weigh somewhat more than .3 of a grain, 
therefore if the bottle would hold three pints, its capacity, solid 
measure, would be rather more than 100 cubic inches, so that if it 
could be perfectly exhausted, it ought to weigh .3 X 100=30 grains 
more when weighed with the stop-cock open, than it does after 
the air has been extracted from it. By using an air-pump instead 
of a syringe, a bottle with a stop-cock may be so nearly exhausted 
of air, as to leave behind no quantity sufficient to interfere in the 
slightest degree with the result of this experiment. 

Different Kinds of Airs or Gases. 

16. Common air, which forms the atmosphere surrounding on 
all sides the earth which we inhabit, was long supposed not only 
to be a simple elementary body, but even after its mechanical pro- 
perties had been investigated, and great progress had been made 
in the study of the laws of nature, very erroneous ideas were re- 
tained concerning the composition of air, and it was imagined 
that all elastic fluids were essentially the same. It is now known 
that atmospheric air is a compound, consisting of two different 
species of air or gas, one of which, called oxygen gas, and 
sometimes vital air, is necessary to the support of animal life ; and 
the other, named nitrogen or azotic gas, when inspired alone, is 
injurious to animals. Both these gases are capable of entering 
into combination with many other bodies of very different kinds, 
and producing compounds, some of which are usually in the solid 
or liquid state, and others in the form of permanent gases. There 
are likewise other gaseous bodies besides oxygen and nitrogen 
which have never been decomposed, and are therefore considered 
as simple forms of matter ; and these, together with the various 
compound gases, constitute a very numerous class of bodies, 
which possess different degrees of elasticity and weight, and by 
their consequent pressure on solids and liquids, produce equili- 
brium or motion ; and hence they are capable of being applied to 
various important purposes. 

17. The peculiar nature and effects of the combinations of the 
gases with each other and with solid and liquid substances can 
only be ascertained by the application of the principles of chemi- 
cal science ; but the action of the gases or airs, so far as it depends 

What is the weight of a cubic foot of air ? 

About how many grains less will a three-pint bottle weigh when ex- 
hausted than when filled with air ? 

What opinion prevailed among the early philosophers in regard to the 
nature of air ? 

How were all gaseous bodies regarded ? 

Of what materials is atmospheric air composed ? 

What analogy have oxygen and nitrogen with other gaseous bodies f 

What differences exist in the mechanical properties of the gases? 

How far does the examination of gaseous bodies belong to the science 
of pneumatics? 



GASES AND VAPOURS. 185 

on their mechanical properties, forms the appropriate subject of 
Pneumatics. 

18. Though atmospheric or common air, as being by far the 
most abundant and generally diffused of all elastic fluids, is there- 
fore usually employed as the medium of pneumatic pressure, yet 
since the recent researches of men of science have made us ac- 
quainted with the variety of those fluids and their several proper- 
ties, it appears that some of them maybe adapted to the purposes 
of art with greater advantage than others, and atmospheric air is 
no longer the only kind of gas made use of as a moving power. 

19. The discovery of elastic fluids much lighter than the atmo- 
sphere has given origin to the art of Aerostation, or soaring through 
the air in an inflated balloon ; the explosion of gunpowder, and the 
projectile force of balls, shells, and other missiles discharged from 
artillery, depends on the elasticity of a peculiar kind of air formed 
by the deflagration of nitre, sulphur and charcoal, composing gun- 
powder; and the combustion or burning together in close vessels 
of oxygen gas with another kind of gas called hydrogen forms 
water, which, being a liquid, nearly the whole space taken up by 
the gases previously to their combustion becomes a vacuum, and 
thus pressure may be produced, and a moving power obtained. 

20. The application of the vapour of water to cause motion by 
the alternate expansion and condensation of steam affords an ex- 
ample of the advantageous adaptation of a non-permanent gas to 
the most important purposes ; and if convenient means can be 
discovered for the liquefaction of common air and other gases by 
pressure and reduced temperature, as appears probable from the re- 
searches of Mr. Faraday and others, it may be expected that ma 
chines will be invented as far superior in some respects to the 
steam-engines now used, as they are to those which were con- 
structed in the early part of the last century. 

21. As the mechanical effects of the different gases when they 
act by pressure must depend on their relative specific gravities, it 
is of importance that those should be accurately ascertained. The 
following table will show the respective weights of equal quanti- 
ties by measure of several elastic fluids, including those which 
are of the greatest importance, on account of their frequent occur- 
rence and the valuable purposes to which they have been applied. 

Weight of 100 cubic inches. Specific gravity. 
Atmospheric air - - 30.5 grains - 1. 

Oxygen Gas - - - 33.8 - 1.111 

Nitrogen Gas - - - 29.25 0.972 

Nitrous Oxide - - - 46.5 - - 1.527 

To what mechanical purposes have the gases other than common air 
been applied ? 

By what species of force is motion impressed on projectiles 1 

How does the alternate formation and condensation of non-permanent 
vapour afford a mechanical agent ? 

How much do 100 cubic inches of common air weigh ) How much 
the same bulk of oxygen ? of nitrogen ? nitrous oxide ? hydrogen ? car- 

Q 2 



186 PNEUMATICS. 

Hydrogen Gas- - - 2.12 - 0.069 

Carbonic Acid - - 46.5 ... 1.529 

Chlorine Gas - - - 76.3 ... 2.500 

Subcarburetted Hydrogen Gas* 16.9 - 0.555 

Carburetted Hydrogen Gas* 29.6 - 0.972 

Steam - 18.8 - - - 0.519 

22. From this table it may be perceived that gaseous bodies 
differ greatly from each other in specific gravity ; chlorine being 
2'| times the weight of common air, and hydrogen only about 
7-100 the weight of that fluid, so that common air is nearly 15 times 
the weight of hydrogen. Steam has but little more than half the 
weight of atmospheric air, and hence it rises through the air, in 
the same manner that a piece of deal or cork rises in water. 

Elasticity of Mr. 

23. The most obvious and effective property of air is its elasti- 
city, to which, with its gravity or weight, are to be attributed the 
phenomena of equilibrium, or motion in bodies under the influence 
of pneumatic pressure. In addition, therefore, to what has been 
already stated concerning these properties, a more detailed inves- 
tigation of their. nature and action will be requisite in order to the 
fuller elucidation of that branch of science now under our notice. 

24. The elasticity of air appears from its resistance to pressure. 
The application of a heavy weight, or any external force to a 
woolpack or a bag filled with twisted horsehair would cause the 
pack or bag to give way, and become more or less contracted, but 
on the removal of the force it would expand to nearly its original 
dimensions.f What thus takes place is manifestly owing to the 

bonic acid ? chlorine ? subcarburetted hydrogen ? carburetted hydrogen ? 
steam ? 

What substance is generally assumed as a standard of comparison in 
stating the specific gravities of the gases ? 

What are the several specific gravities of the gases compared with that 
substance as unity ? 

How many times heavier is common air than hydrogen gas? 

How much lighter is common steam than atmospheric air ? 

What property of air is most important in reference to its mechanical 
agency ? 



* The gases procured from the distillation of coal and from oil con- 
sist principally of subcarburetted hydrogen, or light inflammable air, 
and carburetted hydrogen, or heavy inflammable air. As these gases, 
which are now generally used for lighting streets and shops, are fre- 
quently mixed with other gases, the specific gravity must vary, in dif- 
ferent specimens, with the degree of purity. Coal-gas, after it has been 
purified is found varying in' specific gravity, from .450 to .700 ; while oil- 
gas, which contains a larger proportion of carburetted hydrogen, is much 
heavier, and therefore yields more light in proportion to its bulk. 

f The manner in which elastic bodies act is strikingly illustrated by the 
novel application of spiral springs of iron wire in the construction of 
elastic chairs and beds. Dr. Paris, who notices this invention in his 



ELASTIC FORCE OF AIR. 



187 



" 



form and texture of the included substances ; the particles of which 
are separated by numerous interstices, and therefore readily yield 
to the force applied at the surface, which drives them nearer to- 
gether without destroying their elasticity, or disposition to regain 
their previous situation, and hence they recede from each other, 
when the force which made them approach is withdrawn. A 
bladder filled with air may thus be compressed by squeezing it 
with the hands, and it will swell out again as soon as it is reliev- * 
ed from the pressure, owing to its particles being endowed with 
a power of repulsion; for in proportion as they are left at liberty 
they exhibit a tendency to expand in every direction, so that their 
absolute dispersion through boundless space can only be prevented 
by the influence of pressure. 

25. The elasticity of the air is most convincingly 
demonstrated by the operation of the machine called 
an air-pump, the construction of which is similar in 
principle to that of the syringe. By adapting two 
stop-cocks to a common syringe, and forming by 
means of them a communication with a vessel of 
convenient shape and dimensions, a rude and im- 
perfect kind of air-pump might be contrived, by 
"5«o means °f which air included in the vessel might 
be considerably rarefied or condensed. The effect 
thus produced will appear from the annexed figure, 
in which A B represents a syringe with a solid pis- 
ton, C a cock, which when open, leaves a commu- 
nication between the barrel of the sjmnge and the 
glass globe E ; and D another cock which opens 
a communication with the external air. If now 
we suppose the piston to be at the bottom of the 
barrel, and the cock D shut, then on drawing the piston up 
to A, a part of the air in the globe will rush into the barrel, 
and the whole mass of the included air will become expanded ; 
the cock C is then to be closed and the cock D opened, when 
the piston being pressed to the bottom of the barrel, the air it con- 
tained will be expelled through the open cock; this is next to be 
shut, and the cock C opened, and or. drawing up the piston again, 
the air in the globe will become further rarefied ; and these opera- 
tions, the alternate opening and shutting of the cocks, and raising 
and depressing the piston, may be continued till a high degree of 
rarefication is produced. This apparatus is called an exhausting 
syringe. 

Whence does this property become apparent ? 

What familiar illustration shows the nature of this action.'' 

How is the dispersion of air through the regions of space prevented ? 

What machine demonstrates most satisfactorily the elasticity of air? 

Explain the simplest form of this machine. 

" Philosophy in Sport made Science in Earnest," says, " Down itself can- 
not he more gentle nor springy ; and such beds never require to be shaken 
or mc de." 




> 



188 



PNEUMATICS. 



26. The same apparatus may be employed to effect the con- 
densation of the inclosed air, by drawing- up the piston with the 
cock C shut, and D open, and thrusting down with C open, and 
D shut; for by continuing this process, air would be made to enter 
by the cock D, and be afterwards forced into the globe E. The 
apparatus now takes the name of a condensing syringe ; though 
valves which open and shut by the mere pressure and expan- 
sion of the included air are usually substituted for the stop- 
rocks. Valves are more convenient than stop-cocks, as re- 
quiring less labour and attention on the part of the operator; but 
a much higher degree of exhaustion can be effected by means of 
a syringe furnished with the latter than by using the common ex- 
hausting syringe with valves ; yet these are generally adopted in 
the construction of exhausting and condensing syringes and air- 
pumps, as being much less expensive than stop-cocks, and more 
easily kept in proper order. 

27. The air-pump, as might 
be inferred from its appella- 
tion, is a machine for ex- 
tracting air out of a close 
vessel, and thus producing 
w r ithin it a degree of rare- 
faction nearly approaching to 
a vacuum; it being impos- 
sible, as we shall subse- 
quently show, to form a per- 
fect vacuum, by this or any 
other apparatus ; though the 
ps^j exhaustion may be carried 
so far that the remaining air 




will not at all interfere with the results of our experiments. 

28. The figure in the margin exhibits a section of an air- 
pump, from which it may be perceived that it essentially consists 
of two exhausting syringes, so arranged that they can be worked 
alternately. The syringes are marked A A, and their pistons are 
moved up and down within the barrels, by the racks or toothed 
rods B B, adapted to corresponding teeth on the periphery of the 
wheel C, having a winch or handle M, by which it may be turned 
so as to raise and depress either piston successively. Each of 
the pistons is furnished with a valve by which the air escapes as 
the piston descends, and there are other valves D D, at the bottom 
of each barrel, which become closed by either piston in its de- 
scent, but when it is drawn up, open a passage into the tube E E, 
communicating with the cavity of the glass bell F, called a re- 



What purpose is served by the stop-cocks or valves of an exhausting 
syringe ? 

Is the air-pump adequate to produce perfect exhaustion within a con- 
taining vessel ? 

In what manner is motion usually communicated to the pistons of an 
air-Dumn? 



THE AIR-PUMP. 189 

ceiver. From the tube E passes off another tube G, the extremity 
of which opens into the bell-shaped tube K, within which is a small 
basin H, containing mercury, and the small tube I, closed at the 
upper end only, has its lower end plunged beneath the surface of 
the mercury. At L is a stop-cock, which when closed cuts off 
the communication between the receiver and the syringes, and 
which must therefore be opened while the machine is put in ac- 
tion. Another stop-cock, not shown in the figure, closes a pass- 
age through which the external air may be admitted under the re- 
ceiver, Avhen the result of an experiment has been ascertained. 

29. There is so little difference in the mode of action of the 
air-pump and the exhausting syringe before described that the ef- 
fect of the former will be readily understood. Either syringe in 
turn, by the elevation of its piston, and the consequent closure of 
the piston-valve and opening of the valve D, draws a portion of 
air from the receiver F, through the tube E E ; and the alternate 
depression of each piston, by the elasticity of the air inclosed in 
the barrel, shuts the valve D, and prevents the air from returning 
into the receiver, at the same time that it opens the valve of the 
descending piston, and finds a passage into the upper part of the 
barrel, whence it is expelled by the piston in its next ascent. 
Thus, the reciprocal action of the syringes, by means of the rack- 
work, may be continued, till the requisite degree of rarefaction 
be produced in the air within the receiver. The only part of the 
apparatus requiring further explanation is the air-gauge, consisting 
of the tubes K and I, and the basin of mercury H, with which the 
latter tube is connected. 

30. The air within the tube K, by its pressure on the surface 
of the mercury in the basin, will keep that portion of the same 
fluid in the tube I raised to a height exactly proportioned to the 
density of the included air, which must be the same with that in 
the receiver, in consequence of the communication by the tube G ; 
and thus the height at which the mercury stands in the small tube 
I will serve as a gauge or measure of the elasticity and weight of 
the included air, being always in the inverse ratio of the rarefac- 
tion which has taken place. 

31. It may be proper to add that the edge of the receiver must 
be ground perfectly smooth and level throughout its circumference 
that it may fit closely to the brass plate of the air-pump on which 
it rests ; and that it may prevent the entrance of the air more ef- 
fectually, it must be smeared with grease, or, as is more usual, set 
on a collar of oiled leather, and thus the junction of the receiver 
with the surface below it will be rendered impervious to the air. 

What is the purpose of the mercurial apparatus connected with the 
air-pump ? 

What closes the lower valve of the pump on the descent of the piston 
within the barrel ? 

What ratio is preserved between the height of mercury in the gauge 
and the degree of rarefaction in the receiver ? 

What practical precautions are usually necessary to preserve the rare- 
faction obtained by the action of the air-pump ? 



; 



1 90 PNEUMATICS. 

32. A multitude of experiments, serving 1 to demonstrate the 
elasticity as veil as the weight of air, may be satisfactorily per- 
formed by means of this machine, which was originally invented 
by Otho Guericke, a German philosopher, in the latter part of 
the seventeenth century, and having been rendered more effective 
by the skill and science of Boyle and Hooke, it subsequently un- 
derwent numerous improvements, some of the most important of 
which we owe to the ingenuity of Smeaton, the celebrated engi- 
neer, of Dr. Prince of Salem, in Massachusetts, and Dr. Hare 
of Philadelphia.* But the principle and general plan of this phi- 
losophical instrument, under the various forms in which it has 
been constructed, correspond with the descriptive statement al- 
ready laid before the reader. 

33. The elastic force of atmospheric air may be rendered obvi- 
ous by placing under the receiver of an air-pump a Madder, which 
has been about half filled with air and firmly tied at the neck so 
.as to prevent it from escaping ; for on exhausting the receiver gra 
dually, the bladder will be seen to swell, from the expansion of 
the air within it; and if the exhaustion be continued long enough, 
the bladder will burst, from the elastic force of the air it con- 
tained, no longer counterbalanced by pressure on the external 
surface. 

34. A square or flat glass phial, filled with air, well corked and 
fastened with wire, if placed under the receiver, will crack from 
the expansion of the air within it, as soon as the pressure is with- 
drawn from its surface by the exhaustion of the receiver. A phial 
of the usual shape would resist force applied internally or exter- 
nally, much better than one with flat sides, in consequence of its 
arched figure ; hence the globular or hemispherical shape of the 
receiver, renders it best adapted for its purpose. 

35. Shrivelled apples, prunes, or raisins, with their skins un- 
broken, when placed under a receiver, on the air being exhausted, 
will become plump from the elasticity of the air included in those 
fruits ; and thus a bunch of dried raisins may be made to assume 
the appearance of a fine cluster of grapes, and a similar apparent 
renovation maybe effected on the apples and prunes; but on read- 
mitting the air into the receiver the fruits would all resume the 
wrinkles which betray their age. 

36. If a large glass globe with an open mouth have a piece of 

By whom and at what period was the air-pump invented ? 

Who have contributed towards its improvement? 

How is the elasticity of the air proved by the experiment of the flaccid 
bladder ? 

What will occur when a thin flat or square phial is placed under a re- 
ceiver, and the air exhausted while the phial remains corked ? 

How may shrivelled fruit be temporarily restored to a plump appear- 
ance ? 

Explain the experiment of t\\e glass globe a?id bladder. 

* See Journal of the Franklin Institute, vol. xii. p. 303. 



EXPERIMENTS ON THE ELASTICITY OF AI 



191 



bladder tied over it, so securely that the air within it cannot es- 
cape while the. bladder remains whole, and it be set under a re- 
ceiver, while the air is being- withdrawn from it, that within the 
globe will expand by its elastic force, and raise the bladder to a 
convex shape, distending- it more and more as the exhaustion in- 
creases, till at length the bladder will be ruptured, and the air in 
the globe will expand itself through the receiver. 

37. Let a small syringe, having a weight fastened to the han- 
dle of the piston be closed with a cork at the end, tied down with 
a piece of bladder, so that on pulling' up the piston the air coul 
not enter; then let it be suspended in an inverted position with 
the weight downward, under the receiver of an air-pump ; upon 
extracting part of the air from the receiver, the weight at the han- 
dle will draw down the piston, and on readmitting the air the 
piston will rise again. In this case the partial exhaustion of the 
receiver lessens the elasticity of the included air so considerably 
that it is unable to support the weight ; and on letting in the air 
again, it will recover its elastic force and raise the piston with the 
attached weight, in the same manner as it would be raised hj the 
pressure of the external air. 

38. A very amusing exhibition of the effect pro- 
duced by the elasticity of the air may be made by 
means of the apparatus represented in the margin. 
Hollow glass figures, about an inch and a half in 
length, resembling men or women, must be procured, 
,, ^TM each having a hole in one foot, and the glass must be 
of such thickness that the figures will float near the 
surface of water when they are filled with common 
air. They are then to be immersed in a tall glass 
jar nearly filled with water, and covered on the top 
with a strong bladder, fastened air-tight. If the blad- 
der now be pressed inwards with the finger, the water 
being almost incompressible, and the air quite the re- 
verse, that contained in the little images will yield to 
the compressing force, and becoming contracted, wa- 
!||l|f|»|r]|| ter will enter, and the images thus becoming speci- 
^llllllilEi^ fieally heavier than they were at first will descend 
towards the bottom of the jar ; on the pressure above being re- 
moved, the air in each image recovering its elastic force, will 
expel the water, and the images will rise as before. By forcing 
a little water into one or tw r o of the figures before they are placed 
in the jar, they may easily be made to float at different heights ; 
and thus their motions may be greatly varied, by regulating the 
pressure on the bladder. These diminutive images have been 



How may the syringe and -weight be made to exhibit the alternate ex- 
pansion and contraction of air ? 

Describe the pneumatic toy called the bottle of imps. 

In what manner may the imps be made to rise from the bottom of 
water, and how is the experiment to be explained J 



11)2 PNEIJMAT^;S> 

whimsically called bottle-imps; and their agility must appear 
wonderful enough to those who are ignorant of the cause of it.* 

39. The elasticity of the air may be further illustrated by 
placing an open jar containing a single glass figure, and filled 
with water, under the receiver of an air-pump, only the figure 
must be just heavy enough to sink to the bottom of the jar under 
the usual pressure of the atmosphere. Then on exhausting the 
receiver, and thus diminishing the elasticity and consequent pres- 
sure of the included air, the density of the water remaining the 
same, the figure will gradually rise, as the air becomes more rari- 
fied, till it reaches the surface of the water, where it will float, 
till the air is again admitted into the receiver, on which it will 
descend to the bottom of the jar. 

40. Abundant proof of the compressibility and elasticity of the 
air may be drawn from the consideration of the mode of action 
of the common domestic utensil, a pair of bellows. This will at 
once appear on attending to the effect of the valve or leathern flap. 
This valve rises when the boards are separated, and the air enters 
through the hole in the lower board, which on pressing together 
the boards again becomes closed b)' the falling of the valve, and 
the air having no other vent, makes its exit through the pipe in a 
dense current. 

41. The double bellows, used by blacksmiths and other artisans, 
differs from the .'Machine just described in having an intermediate 
board, which is fixed, while the others are moveable, so that it 
consists of two air-chambers instead of one ; and a hole in the 
middle board, with a valve, suffers the air which has been drawn 
into the lower chamber through the hole below to pass into the 
upper chamber, where it becomes condensed by the pressure of a 
weight fixed to the upper board, and is discharged in a continued 
stream through a pipe connected with the upper chamber. The 
lower board is moveable, and when it sinks by its own weight, 
the valve opens, and shutting again when the board is raised by 
means of a lever or some other contrivance, the air is prevented 
from escaping by the valve-hole, and is therefore forced into the 
upper chamber. 

42. A kind of bellows or blowing machine, constructed entire- 
ly of wood, was invented at Bamberg in Bohemia about 1620, and 
was thence called the Bamberg bellows. It consists of two boxes, 
in the form of cylindrical sectors ; one fitting into the other so as 
not to prevent it from being moved up and down, but without suf- 

How is the common hand bellows constructed ? 

How is a constant stream of air maintained by the double bellows ? 

Of what does the Bamberg bellows consist ? 

* French writers on natural philosophy usually exhibit a single figure 
in describing the counterpart of this experiment. To this little ena- 
melled figure, petite figure d^email, they give the name of Ludion. — V. 
Sigaud de la Fond Elem. de Phys., vol. iii. p. 162. Beudant Traite Elem. 
de Ph vs., p. 306. 



HERO S FOUNTAIN. 



193 



fering the air to escape between the sides of the boxes. It is 
needless to describe it more fully, as the manner in which it acts 
may be easily conceived from what has been stated above. Va- 
rious modifications of this machine have been adopted in esta- 
blishments for smelting metals, and other purposes connected with 
the arts and manufactures. 

43. The effect of air acting by its elastic force on the surface 
of water may be variously exhibited in the formation of jets dPeau^ 
or spouting fountains. Let a strong decanter be filled to about half 
its height with water, and a glass tube of small bore be passed ~~ 
into it nearly to the bottom, and fixed air-tight, going through a 
hole drilled in a cork, with a piece of bladder tied over it and 
ound the tube. This bottle is then to be placed under a tall re- 
ceiver, on the plate of an air-pump ; and on the receiver being 
exhausted, the air within the bottle will expand, and pressing on 
the surface of the water, cause it to issue from the top of the tube 
in a jet, the height of which will be proportioned to the degree 
<>f rarefaction of the air under the receiver. 

44. Compressed air may be made to pro- 
duce a" similar effect, which may be thus dis- 
played : a strong bottle somewhat more than 
half filled with water, as represented in the 
marginal figure, by the line D E, must have 
a tube A C fitting into its neck, and capable— 
of being opened or closed at pleasure, by- 
turning the stop-cock B. A condensing sy- 
ringe* being adapted to the tube at A, and 
the stop-cock opened, air is to be forced into 
the bottle, which rising through the water, 
will by its density press strongly on the sur- 
face of that liquid; then after turning the 
stop-cock the syringe is to be removed, and a small jet-pipe being 
fitted to the tube A, the stop-cock is to be opened, and the elasticity 
of the condensed air in the bottle will drive up the liquid in a jet, 
the height of which will gradually diminish, as the included air, 
by its expansion, approaches nearer and nearer to the density of 
the external air. 

45. A small phial, with a well fitted cork, having a little tube 
or a stem of a tobacco-pipe passed through it, and reaching near- 
ly to the bottom of the phial, partly filled with water, will, on - 
blowing strongly into the bottle through the pipe, exhibit effects 
precisely analogous to those of the apparatus just described. 

46. The machine called Hero's Fountain, resembles in princi- 
ple those noticed above, differing from them only in the manner 
in which the compression and consequently increased elasticity 
of the air is produced. This is effected by means of a column . 

Explain the construction of the fountain in vacuo. 

How is the force of air applied in the compressed air fountain? 

In what respect does Hero's fountain (lifter from the preceding ? 




* See above, 
R 



No. 26. 



194 



PNEUMATICS. 




of water, as will appear from inspection of the 
annexed figure, representing- one of the numer- 
ous forms in which such spouting fountains have 
been constructed. It consists of an open vessel 
A, from which a tube passes downward to the 
vessel B, from the opposite side of which another 
tube forms a communication with a close cavity- 
over the basin C, having a jet-pipe extended al- 
most to the bottom, and open above to the air. 
Water having been introduced into the basin C, 
more water is to be poured into the vessel A, till 
it runs down the tube, and fills the lower part of 
the vessel B, and compressing the air in it, and 
in the other tube and cavity above it, the water 
in the basin C, will, by the elastic force of the 
condensed air, be driven in a jet from the aperture 
at D ; and by adding water to that in the vessel A, the enclosed 
air may be so compressed as to expel nearly all the water from 
the basin C. The principle on which Hero's Fountain acts has 
been heretofore adopted in Germany, in forming machines to raise 
water from mines ; but they have been laid aside since the pro- 
gress of science has led to the construction of far more powerful 
and efficient engines adapted to the same purpose. 

47. A familiar example of the elastic pressure of the air occurs 
in the frothing of bottled ale, porter, cider, and the sparkling or 
creaming of champaigne wine, when uncorked and poured into an 
open vessel ; the air which those liquors contain, on being released 
from its confinement in the bottle, escaping in numerous bubbles 
covering the surface of the liquor. Ginger beer contains a quanti- 
ty of air or gas, formed by a chemical process, and such is its 
elastic force, that if the ginger beer has been properly prepared, 
the included air will drive out the cork with a loud report, as 
soon as the string with which it is tied down is cut through. 
Hence also the bursting of bottles filled with cider, perry, and 
other liquors considerably impregnated with air, when well cork- 
ed and secured with wire. 

48. What is called soda water is manufactured by compressing 
carbonic acid into water by mechanical means ; and it therefore 
can scarcely be preserved except in strong bottles of a peculiar 
form, from which it spouts with violence through the elasticity of 
the condensed gas, as soon as the cork is removed. Air readily 
combines with water, though not to any great extent, under the 
usual pressure of the atmosphere. This will be evident on plac- 
ing a glass of water under the receiver of an air-pump ; for on 
exhausting the receiver the air will issue in a multitude of small 
bubbles from the surface of the water. 



To what purposes has this fountain been applied in mining; operations ? 
In what familiar operations is the elastic force of gaseous matter es- 
caping from a liquid made conspicuous ? 

What is the nature of the preparation called soda ivater? 



RAREFACTION. 195 

49. It has been already stated that a perfect vacuum cannot be 
obtained, even by means of an air-pump of the best construction. 
The impossibility of completely exhausting- the receiver of an air- 
pump ; so far as it is not owing to the imperfection of the machinery, 
depends on the identical property of the aerial fluid which causes 
the air-pump to act : for the elasticity of air is always in the di- 
rect ratio of its density ; so that when half the air is extracted 
from any vessel, the remaining half will expand to fill the whole 
space, its density and elasticity being diminished in the same pro 
portion. Thus if half the air could be exhausted from a receivei 
by the first stroke of the piston, and one-half of what was left b) 
the next stroke, the quantity removed by every subsequent strok- 
must manifestly be but one-half of that removed by the stroke irr 
mediately preceding it : in fact, there must always be a remainder, 
however trifling it must at length become. It will be evident that 
though an indefinitely small quantity of air must thus remain 
after working an air-pump for any imaginable period of time, yet 
that quantity would soon become so extremely inconsiderable as 
to have nearly the effect of a complete vacuum. 

50. Suppose the proportion of capacity between the barrel of 
an air-pump and the receiver to be such, that one-fourth part of 
the air would pass from the latter into the barrel at each stroke 
of its piston, then the quantity remaining in the receiver after the 
fifth stroke would be less than one-fourth of the original quantity ; 
and as the decrease would go on in a geometrical progression, 
thirty strokes of the piston would leave in the receiver only 1-3096 
of the quantity it contained' at first. Hence it will appear that 
if the receiver be not less than the barrel, the smaller the differ- 
ence between the size of the receiver and that of the barrel, the 
more rapidly must the rarefaction of the included air take place; 
and though with a small receiver the air may be highly rarefied 
in a short time, it cannot be entirely withdrawn. 

51 . It must also be observed that the extent to which the rarefaction 
can be effected will be limited by the operation of the rarefied air 
on the valves at the bottom of the barrels ; for as the elasticity of 
the air remaining in the receiver is the cause of the opening of 
those valves, they will at length cease to act, when the exhaustion 
has been carried so far that the expanded air has not elastic force 
enough to overcome the very small degree of resistance caused 
by the weight and friction of the valves. 

52. Another obstacle to the rarefaction beyond a certain limit 
will arise from the resistance to the opening of the piston-valves 

Why cannot a perfect vacuum be obtained by means of the air-pump ? 

What would be the rate of exhaustion if the barrel had one half of the 
capacity of the receiver ? 

State some other relation between the hulks of the cylinder and re- 
ceiver, and compute the degree of exhaustion after a certain number of 
operations. 

What influence has the nature of the lower valve on the extent of rare- 
faction ? 

When must the rarefaction necessarilv cease ? 



198 PNEUMATICS. 

during- the descending- stroke, owing- to the want of sufficient elas- 
ticity in the highly rarefied air to overcome the pressure of the 
atmosphere on those valves. Various improvements have been 
made in the construction of air-pumps, which have considerably 
lessened the imperfections in these machines now stated,* and 
though from the essential properties of air the formation of an 
absolute vacuum in the manner described must be impracticable, 
yet the ingenuity of modern artists has enabled us to produce 
within a receiver any degree of exhaustion requisite for the most 
delicate and interesting experiments. 

Weight of the Air. 

53. The phenomena depending on the influence of gravitation 
on air, and its consequent gravity or weight, are of equal im- 
portance with those arising from its elasticity ; and the subjec* 
therefore demands a more extended investigation than has been 
already afforded to it. 

54. Direct evidence of the weight or ponderosity of air may 
be easily obtained by means of an air-pump. For by ascertain- 
ing the weight of a bottle of known capacity before and after it 
has been exhausted of the air contained in it, the loss of weight 
after exhaustion would show the gravitating force of the air which 
had been extracted from it, and if the experiment be accurately 
performed it would appear that a cubic foot of air would weigh 
523 grains. The same quantity by measure of water would weigh 
1000 ounces avoirdupois ; hence it must follow that water lias 
about 840 times the weight of air, bulk for bulk ; and this result 
corresponds sufficiently with the estimate of the specific gravity 
of atmospheric air compared with that of water, as stated in the 
table of specific gravities, in the treatise on Hydrostatics-! 

55. As air then has a determinate weight like all other ponder- 
able kinds of matter, it must produce pressure in the same man- 
ner as other heavy bodies, and that in proportion to its mass and 
specific gravity. The weight of 1000 cubic inches of atmospheric 
air must, from what is stated above, be greater than that of a 
single cubic inch of water, and consequently if the pressure of 
such a mass of air could be made to act on a small surface, it 
would produce a greater effect than the pressure of a cubic inch of 

What other obstacle to rarefaction exists in the construction of the 
air-pump? 

In what manner may the air-pump be employed to ascertain the weight 
of the air? 

By what number of times does the weight of water exceed that of air? 



* Such is the object of Dr. Prince's improvement, who makes use of 
a subsidiary piston to take off the pressure above the main pistons, after 
the exhaustion is nearly completed. — Ed. 

t See Hydrostatics, No. 88. 



ATMOSPHERICAL PRESSURE. 197 

water. Now the most direct mode of causing- the pressure of a 
given bulk of air to act by its gravity on a surface of a certain ex- 
tent would be, by forming a cylindrical or square column of air, 
the base of which should be exactly of the extent required. This 
could not be conveniently effected by artificial means, except in 
columns the height of which was but inconsiderable ; but in the 
atmosphere around us nature presents a mass of air of great alti- 
tude, the vertical pressure of which on any given space may be 
ascertained by direct experiment. 

56. A receiver, or any other air-tight vessel, placed on the plate 
of an air-pump, would become fixed to it by the exhaustion of the 
included air, in consequence of the atmospheric pressure on its>^ 
surface. Some idea of the amount of this compressing force may 
be obtained by placing the palm of the hand over the top of a 
glass cylinder open at both ends, the lower opening resting on the 
plate of an air-pump, and the upper opening being covered by the 
hand so closely as to prevent the air from entering in that direc- 
tion, the cylinder being partially exhausted the weight of the 
atmosphere pressing on the back of the hand would not only be 
sensibly felt, but would also be found to be so considerable before 
complete exhaustion had been effected, as soon to occasion pain 
and inconvenience. Reckoning the weight of the atmosphere 
upon every square inch of surface, to be fifteen pounds, the pres- 
sure on the hand placed over an exhausted receiver, the top of which 
it would just cover, would be equal to about sixty pounds. 

57. A more exact estimate of the weight of the 
atmosphere may be formed by attending to the result 
of an experiment to show its effect on the surface of 
two hollow hemispheres, from which the air has been *~ 
extracted by means of an air-pump or exhausting 
syringe. Thrse hemispheres, constructed of brass, 
should be furnished with handles, or hooks, by means 
of which they may be suspended ; one of which 
may. be fixed, but the other should be removable. 
In the tubular neck to which this handle is screwed 
is a stop-cock, which being opened, and the handle 
<g3) removed, the hemisphere is to be screwed on the 

pump-plate, or on to an exhausting syringe ; and the 
other hemisphere having been fitted to it, a vacuum is to be form- 
ed in the interior by working the pump. The stop-cock must 
then be turned so as to prevent the re-entrance of air, and on un- 
screwing the brass globe, and refixing the handle, it will be found 
that the hemispheres composing it are firmly united by the pres- 
sure of the external air. Suppose the diameter of the globe to 

How might we conceive the pressure of a given hulk of air acting hy 
its weight alone to be exercised ? 

With what illustration of this subject does nature furnish us ? 

What causes the adhesion of an exhausted receiver to the plate of an 
air-pump .' 

How is the correctness of this explanation made apparent ? 
u 2 




IDS PNEUMATICS. 

be 6 inches, the surface of a section through the centre would be 
about 28 inches square; and hence the pressure of the air upon 
one square inch being 1 known, the force requisite to separate the 
hemispheres, supposing- the exhaustion to be nearly complete, 
might easily be computed. 

58. This is usually termed the Magdeburg experiment, it hav 
ing been originally contrived by Otho Guericke, of Magdeburg 
the inventor of the air-pump ; and it appears to have led him to 
that important discovery. For the manner in which he originally 
conducted the experiment was by filling the space included be 
tween the hemispheres, when pressed together, with water to ex 
pel the air, and then pumping out the water, while the air wa* 
prevented from re-entering by turning a stop-cock. Having thus 
ascertained the fact of the existence qf atmospheric pressure to a 
great degree, he proceeded to the invention of the air-pump, by 
means of which the exhaustion of the joined hemispheres could 
be much more readily and conveniently effected than by the operose 
process he had at first adopted. This ingenious philosopher 
operated with two copper hemispheres, nearly a Magdeburg ell* 
in diameter ; and the amount of pressure on such an extent of sur- 
face was so great, that when the interior cavity had been exhaust- 
ed, the separation of the hemispheres could not be effected by the 
strength of twenty-four horses, twelve being harnessed together 
on each side, and dragging in opposite directions. 

59. That the weight of the atmosphere is always pro- 
portioned to the vertical height of the column of air 
pressing on any extent of surface, may be demonstrated 
by means of a glass tube bent as represented in the mar- 
gin, and open at both ends. The diameter of the tube 
being the same throughout, if mercury be poured into it, 
it will rise to the same height, D C, in either part of the 
tube. Then let the extremity, A, be closed by placing 
over it a piece of moistened bladder, firmly secured by 
melted resin or sealingwax ; and the mercury pressed on by the 
air above it, of the common density of the atmosphere, would 
always remain at the same height, D ; but the column of mercury 
in the other part of the tube having its surface exposed, would 
rise or sink with the variation in density of the atmosphere. Thus 
if such a tube were carried to the top of any high tower or moun- 
tain, the column of air would be shortened by a space equal to 
the height of the situation and the mercury, in some degree re- 
Describe the manner of proving the pressure of air acting by its weight 
on the Magdeburg hemispheres. 

How did Guericke at first produce the vacuum in his hemispheres? 
What account is given of the size and efficacy of his apparatus ? 
In what manner can we prove what pressure the air exercises on the 
exterior surfaces of bodies ? 

* See Winkler's Elements of Nat. Philosophy, Eng. Tr.. 1757, vol. i. 
p. 131. 




THE BAROMETER. ll>9 

lieved from pressure, would rise in the space C B. On the con- 
trary, if the tube could be removed into a deep mine, the mercury 
on the open side would sink below C, being pressed by a loftier 
column of air than when at the surface, where the height of the 
mercury was first noted. 

60. Such an instrument as that just described would be a 
species of barometer,* since it would indicate the varying weight 
of the atmosphere. But the instrument to which the appellation 
of barometer has been given is differently constructed, and better 
adapted to afford a correct estimate of the amount of atmospheric 
pressure at different times, or under varying circumstances. 

61. The invention of this valuable instrument appears to be justly 
attributed to Torricelli, professor of mathematics at Florence, in 
the earlier part of the seventeenth century. He was the pupil of 
the celebrated Galileo, who seems to have been the first among 
modern philosophers who had any idea that air possessed the pro- 
perty of weight; though he was not aware of the mode of its 
operation in producing atmospheric pressure, and the numerous 
phenomena constantly resulting from it. 

62. It had been accidentally observed that in raising water by 
means of a pump, the height to which it could be drawn in what 
is called the suction-pipe never much exceeded 33 feet; since 
when the piston of a pump was elevated more than about that 
height above the surface of the water in the pump-well, the liquid 
no longer followed the piston. The drawing up of the piston of 
course torms a vacuum in the pipe below it, and the consequent 
rising of the water into the void space was accounted for, or ra- 
ther attempted to be explained, by the philosophers of the six- 
teenth century, by the hypothetical principle that " Nature abhors 
a vacuum," and therefore causes the water to ascend in order to 
prevent the vacuum from taking place. 

63. The dogma of Nature's abhorrence of a vacuum is a com- 
plete absurdity ; and the phrase was invented, like many others, 
some of which are still current, to conceal the ignorance of those 
who pretended to universal knowledge. It was, however, gene- 
rally adopted at the period just mentioned ; and till it was disco- 
vered that, when a vacuum was actually formed in the suction- 
pipe of a pump, water would not rise to fill it much above 33 feet, 
no one seems to have thought of questioning the propriety of the 
current opinion on the subject. 

What is the nature and purpose of the barometer ? 
Who was the inventor of that instrument ? 
Who first conceived the idea that air possesses weight ? 
By what expression did ancient philosophers explain the rising of water 
in a common pump ? 

In what light are we to view this expression ? 

* This term signifies a measure of weight, from the Greek B»jo k -, a 
weight, and Ms-r e oi/, a measure. The instrument described in the text 
would bear a nearer relation to Adie'ssympiezometer than to the com- 
raon barometer. — Ed. 



200 PNEUMATICS. 

64. Some engineers at Florence rinding themselves foiled in an 
attempt to raise water by a pump from a well of greater depth 
than usual, applied to Galileo for advice as to the means of raising 
water to a greater height than 33 feet, or at least for an explana- 
tion of the cause of a phenomenon which they could not reconcile 
with the generally received hypothesis concerning the ascent of 
water in the suction-pipe of a pump. Galileo is said to have told 
the inquirers that " Nature's abhorrence of a vacuum did not ex- 
tend to distances greater than 33 feet, and therefore that at that 
point her efforts ceased." It has been questioned whether the 
philosopher really expressed himself in this manner, though the 
story has often been repeated ; and it may at all events be con- 
cluded that if he gave such an answer to those who applied to 
him, he could hardly have considered it as a satisfactory solution 
of the difficulty which had been started. Accordingly in his 
writings he attempts to account for the phenomenon on other 
principles, but the real cause of it seems to have eluded his pene- 
tration. 

65. Probably the discussions to which this circumstance gave 
rise suggested to Torricelli the idea that the ascent of water in 
the suction-pipe of a pump was caused solely by the pressure of 
the atmosphere on the water in the well, and that as the weight 
of the atmosphere at the earth's surface could never vary to any 
great extent, it therefore never greatly exceeded what would be 
sufficient to raise a column of water in a vacuum to the height of 
33 feet. The happy thought occurred to him of verifying his con- 
jecture by making an experiment with a fluid much heavier than 
water, as he perceived that if the ascent of water depended on at- 
mospheric pressure, the same pressure on the heavier fluid would 
raise a column of it to a proportionally inferior height. With 
this view he fixed on mercury, as the heaviest fluid known, at 
common temperatures ; and having procured a glass tube, open at 
one end, he filled it with mercury, the specific gravity of which 
compared with that of water was as 13^ to 1 ; then immersing the 
open end of the tube in a small jar of mercury, and suffering a 
communication to take place between the mercury in the tube and 
that in the jar, he observed that the fluid sunk till it stood in the 
tube just 30 inches above the level of that in the jar below. This 
experiment was so far completely satisfactory ; for as 13^ : 1 : : 33 
feet : 2^ feet = 30 inches ; thus the weight of the atmosphere 
pressing on any given surface was found to be equal to that of a co- 
lumn of water of the same extent at the base and 33 feet in height, 
or of a similar column of mercury only 30 inches-in height. 

What is said to have been the reply of Galileo to inquiries on this sub- 
ject f 

Did that philosopher understand the true cause of the rise of fluids into 
an exhausted tube ? 

To whom do we owe the true explanation of this subject ? 

In what manner did Torricelli demonstrate the correctness of his views 
in regard to the pressure of the air ? 



THE BAROMETER. 201 

66. The barometer now in general use as a weather-glass is 
nothing more than a tube of proper length filled with mercury, and 
either dipped at the open end in a small cup of the same fluid, or 
else having the open end curved upwards, so that the mercury- 
may be exposed to the pressure of the atmosphere : a scale of 
inches also is adapted to the upper part of the tube, extending 
from 27 to 32 inches, that it may appear by inspection at what 
height the mercury stands under the pressure of the atmosphere 
at any particular time. This useful instrument was at first called 
the Torricellian tube, from the name of the discoverer of the prin- 
ciple on which its action depends ; but it subsequently received 
the designation of a barometer, now universally adopted. 

67. After the effect of atmospheric weight and consequent pres- 
sure had been ascertained by the decisive experiments of Torri- 
celli, the subject was further investigated in France, chiefly by 
the distinguished philosopher Pascal, and by Father Mersenne, 
in 1647. The former reflecting on the effects of atmospheric pres- 
sure, it occurred to him that the weight of the column of air, de- 
pending on its vertical height, must be greatest in low situations, 
and decrease in ascending an eminence. To try this principle by 
the test of experiment, he requested a friend who resided in Au- 
vergne, to ascertain the relative heights of a barometrical column 
at the bottom, and afterwards at the top of the Puy de Dome, a 
high mountain, situated in that province of France. The effect 
took place as Pascal had anticipated ; and he himself subse- 
quently made corresponding observations on a barometer, removed 
from the level of the street in Paris to the summit of a lofty 
church-tower. 

68. As a philosophical instrument, the barometer is highly use 
ful, not only for the purpose of ascertaining the daily and hourly 
variations which are taking place in the atmosphere in any given 
situation, arising from causes connected with the science of me- 
teorology, and for other purposes of a similar nature ; but likewise 
as affording means for accurately estimating the heights of moun- 
tains, or in fact of any places whatever above the level of the sea. 
For either of these purposes, however, it is necessary that a baro- 
meter should be very carefully and accurately constructed ; and 
in making observations by means of it, especially in the measure- 
ment of heights, various precautions are required, and the effect 
of temperature in particular must be taken into the account in 
making any calculations. 

69. It must hence be obvious, that as a weather glass, the uti 
lity of such instruments as are commonly used must be extremely 

Describe the manner of constructing the barometer. 
By what name was this instrument formerly known ? 
What application of the barometer was made by Pascal ? 
In what manner was his principle verified? 

To what particular purposes is the barometer applied in meteorology.. 
What particularly requires attention in the measurement of heights by 
the barometer ? 



202 PNEUMATICS. 

limited ; for as the height of the mercury at any time must depend 
partly on the elevation of the place of observation above the level 
of the sea, no correct judgment can be formed relative to the den- 
sity of the atmosphere, as affecting the state of the weather with- 
out reference to the situation of the instrument at the time of 
making the observation ; and a series of observations at any given 
place would be required in order to enable a person to form a pro- 
bable opinion of the change of weather to be expected after the 
rising or falling of the mercury. 

70. One source of imperfection in the instrument, which ren- 
ders it difficult to determine the extent of those slight variations 
in the height of the mercurial column which are yet interesting to 
the meteorological observer, has led to some peculiarities of con- 
struction, by means of which the scale of observation might be 
enlarged, and minute changes in the height of the mercury be ren- 
dered obvious. One method of effecting this purpose is by means 
of what is called a wheel barometer, the external ap- 
pearance of which few persons can be unacquainted 
with, as such instruments are generally preferred for 
domestic use. 

70. The construction of the wheel-barometer may 
be thus described, with reference to the figure in the 
margin. It consists of a tube, ABC, hermetically 
sealed at A, and open at C ; and of such a length that 
the distance from C to A may be about 32 inches. The 
tube must be entirely filled with mercury, which on 
placing it in a vertical position will subside in the part 
A B, till the difference of the levels E and F will be 
equal to the height of a column of mercury which will balance 
the weight of the atmosphere, so that any change of pressure will 
have an equal effect on the mercury at E and F, and thus through 
whatever space the fluid may rise at E, it will be depressed to 
the same extent at F. Upon the surface of the mercury at F floats 
a small ball of iron, suspended by a strong thread over a pulley 
P, and to the other end of the thread is attached the weight W, 
not so heavy as the floating ball. The axis of the pulley passes 
through the centre of a large graduated circle G, and carries an 
index H, which revolves as the pulley turns round. The weight 
W being just heavy enough to counterbalance the iron ball and 
overcome the friction of the pulley, the iron ball rises and falls 
freely, as the surface of the mercury on which it floats is elevated 
or depressed by the weight of the air. Now if the circumference 
of the wheel P be 2 inches, then one entire revolution will corre- 

Why is the barometer, as commonly constructed, ill adapted to the 
purposes of indicating the state of weather ? 

How has it been found practicable to enlarge the scale of barometric 
variations, so as to read slight differences ? 

Give a description of the wheel-barometer. 

What is the purpose of the weight suspended on the exterior end ot 
the cord ? 




THE WATER-BAROMETER. 2\)S 

spond to an alteration of level amounting to 2 inches at F, and 
therefore to an alteration of 4 inches in the height of the barome- 
tric column. And as the graduated circle may conveniently be 40 
inches in circumference, 10 inches of that circle will correspond 
to I inch of the column, and 1 inch of the circle to 1-10 of an inch 
of the column ; so that variations, amounting to much less than 
the tenth of an inch will be distinctly perceptible. 

72. As already stated, the utility of the barometer as a weather- 
glass must depend on certain circumstances, with reference to the 
situation of the observer; and not the least attention ought to be 
paid to the words "rain," "fair," "changeable," &c, frequently 
engraved on the plate of a barometer, as they will be found to af- 
ford no certain indications of the correspondence between the 
heights marked and the state of the weather. 

73. General rules for calculating changes in the weather from 
the barometer can seldom be adapted to all situations ; and there- 
fore those who may be desirous of obtaining the means for form- 
ing a correct judgment, as to subsequent alterations in the state 
of the atmosphere, from the indications of the degree of atmosphe- 
ric pressure at any time afforded by the barometer, must devote 
much attention to the subject; without which, written rules would 
only mislead the observer, and long application to the practical 
study of the instrument would render rules unnecessary. One 
circumstance, however, may be worth mentioning, which is, that 
changes of weather are indicated not so much by the actual height 
of the barometrical column, as by its variation of height, and the 
manner in which that variation takes place. 

74. Among the methods which have been adopted to obtain the 
most accurate estimates of the effect of atmospheric pressure may 
be noticed the compound barometer, in which water is added to 
the mercury in the tube, and the mean height of the barometrical 
column being thus augmented, the variations which arise from 
the varying weight of the air will be more considerable than in a 
common barometer, and therefore may be more distinctly observ- 
ed. Such instruments, however, are liable to certain defects and 
disadvantages, which render them inferior upon the whole to 
those of the usual construction. 

75. A barometrical column, composed of water alone, from its 
extreme sensibility to changes of atmospheric pressure, must af- 
ford much greater facility for noticing the more minute alterations 
which are found to be constantly occurring than the mercurial ba- 
rometer. But a water barometer must necessarily be a most un- 
wieldy machine, and consequently could be adopted in but few 
situations, even where the expense and inconvenience attending 
its construction might be of little importance. 

What reliance is to be placed on the prognostics of weather sometimes 
found on the scales of barometers ? 

What circumstance, in regard to changes of weather, deserves parti- 
cular attention ? What advantage is possessed by the column composed 
of water and mercury ? 



204 PNEUMATICS. 

76. M. Pascal, whose philosophical researches have been al- 
ready noticed, made some interesting experiments at Rouen, in 
Normandy, in which he, by means of glass tubes, 40 feet in 
length, ascertained the effect of the pressure of the atmosphere on 
water, and also on wine ; and he found that when mercury stood 
in the common barometer at the height of 2 French feet 3^ inches, 
water was raised in one of his tubes to the height of about 31 1-9 
feet, and wine to that of 31f. Thus, though' the difference of 
specific gravity in these two liquids must have been but inconsi- 
derable, yet it occasioned a sensible difference in the manner in 
which they were affected by atmospheric pressure. The experi- 
ment on water was repeated by Roger Cotes, professor of philo- 
sophy at Cambridge, England, in the beginning of the last cen- 
tury ; but in both cases the object was merely that of a temporary 
exhibition for the purpose of distinctly demonstrating the operation 
of aerial gravity and pressure. 

77. A permanent water-barometer, however, has been erected 
by order of the Royal Society of London, in the hall of entrance 
to their apartments, the tube extending upwards in the well of a 
winding staircase. It consists of a glass tube 40 feet in length, 
and 1 inch in diameter at the lower end, nearly cylindrical through- 
out, being only a little narrower at the upper extremity than it is 
below. This instrument is well adapted to show the various pe- 
riodical alterations, or as they have been termed, oscillations of 
the atmospherical column, and some observations, with tables form- 
ed from them, have already been laid before the Royal Society, 
by Mr. Daniell. It has been noticed, that the rise and fall of the 
column of water in this barometer precedes, by one hour, the cor- 
responding changes in a mercurial barometer; and it is stated 
that in windy weather the water is in perpetual motion, its fluc- 
tuations in the tube having been compared to the breathing of an 
animal.* 

78. It has been already observed, that the elasticity of the air 
is always in the direct ratio of its density ; or in other words, that 
the greater the density of any portion of air, the greater will be 
the degree of elastic force which it is capable of exerting. The 
best modern air-pumps are so constructed as to serve for the 
condensation as well as the rarefaction of air; but for the former 
purpose, a condensing syringe may likewise be employed ; and 
either method may be adopted in making experiments on the elas- 
ticity of compressed air. 

79. Among the most interesting applications of the force of air 

What relation did Pascal find between the heights of columns of wine 
and of water equivalent to the weight of the atmosphere ? 

In what peculiar manner is the water barometer found to be affected ? 

What advantage does it possess over the mercurial barometer, in regard 
to the indication of diurnal fluctuations ? 

In what ways may the artificial condensation of air be effected ? 

* Arcana of Science, 1833, pp. 253, 264. 



THE AIR-GUN. 205 

in a slate of high condensation is that of projecting by such means 
bullets or other missiles from an air gun. It is somewhat re- 
markable, that this instrument appears to have been in use before 
the discovery of the air-pump or the barometer ; for it is mentioned 
in a work entitled " Elemens d'Artillerie," written by David Ri- 
vaut, who was preceptor to Louis XIII. of France, and he as- 
cribes the invention to Marin of Lisieux, in Normandy, who pre- 
sented an air-gun to Henry IV. It is also stated, that an air-gun 
was preserved in the armory of Schmettau, on which was the date 
1474. But these instruments were far inferior to modern air-guns, 
from which they must have differed considerably in the mode of 
construction. 

80. The air-gun, like the common gun or musket, consists partly 
of a long metal tube adapted to receive' a ball, but the breech end 
of the tube or barrel has an opening to admit condensed air be- 
hind the ball, which, acting by its elastic force, propels it with a 
velocity, proportioned to the degree of condensation of the air. 
Though the effect is produced in the manner just described in all 
air guns, yet the mechanism or arrangement by which the admis- 
sion of the air is regulated varies in different instruments. Some 
of them are furnished with a syringe for compressing the air, in- 
cluded within the butt of the gun, and there is an exterior tube 
surrounding the barrel, so that the air is forced into the space be- 
tween the tubes, and the ball having been introduced into the bar- 
rel which it fits closely, a valve is opened by pressing on a knob 
or trigger, and the air rushes from the cavity formed by the outer 
tube into the chamber behind the ball, which it expels from the 
barrel, continuing to act upon it by its exparisive force till the ball 
has passed from the mouth of the air-gun. Other instruments 
have but one tube, for the reception of the ball ; and the air is 
compressed by a condensing syringe into a strong brass or copper 
globe, which when filled, can be detached from the syringe, and 
screwed to the butt of the gun, and by a contrivance similar to 
that already described, a bullet can be discharged, by drawing a 
trigger. The butt may be made to hold a magazine of balls, 
which can be admitted one at a time into the chamber, and a por- 
tion of the condensed air escaping on opening the valve, several 
balls may be projected from the air-gun in succession, but in this 
case, as each discharge will diminish the density and elasticity 
of the remaining air, the velocity and effective force of the balls 
will also progressively decrease. 

81. From what has been stated relative to the density and elas- 
ticity of air, it will follow, that all bodies on the surface of the 

What are some of the important applications of condensation ? 

What are the essential parts of the air-gun ? 

To what is the velocity of the hall proportioned ? 

What two different arrangements of parts are occasionally applied for 
retaining the condensed air? 

Can this instrument propel, -with equal velocities, several balls in suc- 
cession, without renewing the charge of air 5 

5 



206 PNEUMATICS. 

earth, sustain a pressure from the superincumbent atmosphere 
equal to the weight of a column of water, about 34 feet in height, 
with a base corresponding in extent to that of the body or bodies 
pressed upon. This pressure may be estimated at from 14 to 15 
pounds on every square inch of surface, being the weight of a co- 
lumn of mercury 30 inches high, and 1 inch square at the base. 

82. Hence it must be evident that every human being constant- 
ly has pressing on the body in every direction a weight equal to 
15 times as many pounds as there are square inches on the sur- 
face of that body. Suppose then the surface of a man's body to 
measure 2000 square inches, the force of the atmosphere pressing 
on that surface would be equal to 30,000 pounds. It may appear 
unaccountable that so vast a pressure should be perpetually in 
operation, without our being sensible of the weight or experienc- 
ing any inconvenience from it. This however is owing to the 
uniform manner in which the force acts in all directions, so that 
the body is supported by the pressure on one side against the 
equal pressure on that which is opposite ; and it is only when the 
equilibrium is destroyed by removing the force in one direction, 
that its effects become perceptible, as is shown by an experiment 
previously described, in which the hand is exposed to atmosphe- 
ric pressure by placing it over a partially exhausted receiver. All 
the cavities of the body also are either filled with air or with 
denser fluids, so that they resist compression from the external air 
as perfectly as the firmest solids. 

83. Some idea of the weight of the whole atmosphere, encom- 
passing the earth on every side, may be formed from a calculation 
which has been made to determine what must be the diameter of 
a sphere of lead, the weight of which would be equal to that of 
the entire atmosphere ; and from which it appears that the sphere 
must have a diameter nearly 60 miles in length ; which would 
correspond in weight with a mass of water sufficient to cover the 
whole surface of the earth to the height of 34 feet. 

84. It is an interesting matter of speculation to what height the 
atmosphere extends from the surface of the earth. If the density 
of the atmospheric column were uniform, its vertical height might 
be readily calculated ; for as water is nearly 850 times heavier 
than air of the common density, and a column of water 34 feet 
high is equivalent to an atmospherical column having a base of the 
same extent, it is evident that the height of such a column of air 
of uniform density must be 850 times 34 feet, or 850x34=28,900 

What amount of atmospheric pressure is sustained by all bodies on the 
surface of the earth ? 

What pressure is applied to the body of a person of ordinary size? 

How is the body enabled to sustain this pressure without inconvenience ? 

What would be the diameter of a sphere of lead equal in weight to the 
whole atmosphere of our globe ? 

To how thick a stratum of water over the whole globe would this be 
equivalent ? 

How may we calculate the height of an atmosphere of uniform density 
equal in weight to that of the earth ? 






ALTITUDE OF THE ATMOSPHERE. 207 

=5 miles 833 yards and 1 foot, or nearly 5^ miles. But the den- 
sity of the air varies at different distances from the surface of the 
earth, in consequence of its elasticity. 

85. Air maybe conceived to consist of innumerable strata or 
layers, forming a concentric shell, surrounding the solid globe we 
inhabit ; and the lowest stratum being compressed by the whole 
weight of the superincumbent mass, must necessarily be more 
dense than the next above it, and the density decreasing in pro- 
portion to the increase of height or distance from the earth's sur- 
face, no definite limit can be assigned to the extent of the atmo- 
sphere. 

86. Cotes, in his Hydrostatical Lectures, has stated the relative 
density of the atmosphere at different heights, as deduced from a 
comparison of the specific gravity of air at the common level of 
the earth's surface with that of air at a certain elevation as ascer- 
tained by means of the barometer. Thus the rarity of the air being 
four times greater at the altitude of seven miles than at the sur- 
face, and the rarity of the air augmenting in a geometrical pro- 
gression, while the altitude increases in an arithmetical progres- 
sion, it will follow that at the height of 14 miles the atmosphere 
would be 16 times rarer than at the surface, at 21 miles 64 times 
rarer, at 28 miles 256 times, at 35 miles 1024 times, at 70 miles 
about a million of times, at 210 miles a million of millions of mil- 
lions of times, supposing air to be capable of indefinite expansion. 
Hence, also, at the altitude of 500 miles, if the air could continue 
to expand at the same rate, a cubic inch of the common density 
would be dilated through a greater space than a sphere equal in 
diameter to the orbit of Saturn.* This, however, is a purely hy- 
pothetical estimate, for it is founded on the presumed infinite 
divisibility of matter. 

87. The observations of Dr. Wollaston, "On the Finite Extent 
of the Atmosphere," f tend to prove that air consists of ultimate 
indivisible particles ; and the expansion of a medium composed 
of such particles must cease at a certain point where the force of 
gravity acting downwards, upon a single particle, would be equal 
to the resistance arising from the elastic or repulsive force of the 
medium. At such an altitude, therefore, the elasticity of the 
atmosphere would be completely extinguished, and thus a physi- 

How may we conceive the atmosphere to he arranged upon the surface 
of the globe ? 

What limit can be assigned to the height of the atmosphere ? 

State the calculated progressive rarefi cation of air as dependent on 
elevation. 

On what supposed property of air is this calculation founded ? 

What views did Dr. Wollaston advance on this subject ? 

What equality of forces would limit the expansion of air? 

* See Cotes's Hydrostatical and Pneumatical Lectures. Sec. edit. 
Cambridge, 1747, p. 124. 

f Abstracts of Papers in the Philos. Trans., vol. ii. pp. 160— 162. 



208 PNEUMATICS. 

cal limit might be assigned beyond which it could not possibly 
extend. 

88. In making calculations relative to the density of the air at 
different heights, or forming rules for the determination of the cor- 
respondence between atmospheric altitude and pressure, for prac- 
tical purposes, such as the measuring of eminences by means of 
the barometer, several circumstances must be taken into the ac- 
count. Thus it is not only necessary that the exact height of the 
mercurial column at different levels should be ascertained, but due 
regard must also be had to the influence of temperature, the effect 
of vapour suspended in the air, and the latitude of the eminence 
whose height is to be determined. The indefatigable spirit of 
research of modern experimental philosophers and mathematicians 
has triumphed over these difficulties so far as to have furnished 
us with general principles and formulae, by the application of 
which to the results of carefully conducted experiments, the per- 
pendicular heights of the principal mountains in every part of the 
world have been discovered. 

89. From calculations founded on the barometical formula con- 
trived by the celebrated mathematician, Laplace, and adapted to 
the estimation of heights, it appears that at the elevation of 
52,986 metres, French measure, or 173,795 English feet,* the rarity 
of the air as equal to the utmost degree of rarefaction which can 
be obtained in the exhausted receiver of an air-pump. This mani- 
festly connot be the extreme altitude of the atmospheric column, 
nor is it possible to decide that point with certainty. But it ap- 
pears from the observations of astronomers on the duration of 
twilight and the magnitude of the shadow of the earth by which 
the moon is eclipsed, that the rays of light from the sun are 
affected by the medium through which they pass at the distance 
of from 40 to 50 miles from the earth's surface ;j and therefore it 
may be reasonably inferred that the atmosphere extends to the 
altitude of at least 45 miles above the level of the sea. 

90. The pressure of the air arising from the joint effect of elas- 
ticity and weight is the cause of a great number of phenomena 
constantly taking place around us, and immediately depending on 
the operations of nature or art. It is thus that the effect of the 
instrument called a sucker, used by schoolboys, is to be explain- 
ed. It consists of a disk of moistened leather, with a string 
by which it may be suspended with any weight attached to it 

What three circumstances are to be taken into account in measuring 
heights by barometric observations ? 

At what height has Laplace calculated that air will have as great a 
rarity as it is possible to produce by the air-pump ? 

What height of our atmosphere is deduced from the observations of 
astronomers on the duration of twilight, and the magnitude of shadows 
in eclipses of the moon ? 

* A French metre is 39.37" inches English measure, or 3.28 feet, 
f See Treatise on Optics. 



EFFECTS OF ATMOSPHERIC PRESSURE. 209 

and as its smooth moist surface may be pressed so closely against 
the flat side of a stone or other body, that the air cannot enter be- 
tween them, the weight of the atmosphere, pressing on the upper 
surface of the leather, makes it adhere so strongly that a stone 
of weight proportioned to the extent of the disk of leather may be 
raised by lifting the string. If the sucker could act with full 
effect, a disk an inch square would support the weight of 14 
pounds; but the practical effect of the instrument must be variable, 
even supposing that it was accurately constructed. 

91. Whenever surfaces are brought into such close contact that 
the air cannot insinuate itself between them, they will be pressed 
together with a force corresponding to the extent of the surface 
of contact. Hence glass-grinders and polishers of marble find 
that the substances on which they are operating by friction, when 
reduced to a state of extreme smoothness, become united by atmo- 
speric pressure so firmly that great exertion is required to sepa- 
rate them, and the circumstance is the cause of considerable in- 
convenience. 

92. The adhesion of snails, periwinkles, limpets, and some 
other crustaceous animals, to rocks and stones, is effected on the 
same principle. The surfaces of their shells at the opening are 
capable of being exactly fitted to any plane surface; these ani- 
mals have the power of producing a vacuum within their shells 
when thus fixed, and the atmosphere consequently presses on 
them with a force proportioned to the extent of exterior surface. 
It is thus, too, that a common house-fly is enabled to run with 
great facility up a perpendicular pane of glass, or on the under 
side of a horizontal plane, as the ceiling of a room. The feet of 

( the insect are provided with cavities, the sides of which being 
adapted to the surface of glass, &c, by some internal mechanism 
the cavities are exhausted, and the pressure of the atmosphere on 
the minute surface of the feet supports the insect against the 
power of gravitation. That such small animals may be thus sus- 
tained will probably appear less extraordinary than that a similar 
power of running up a perpendicular plane should be possessed by 
a much larger creature. 

93. But Sir Everard Home, who, by means of microscopical 
observations explained the structure of the fly's foot, as connected 
with its mode of progression on walls and windows, also investi- 
gated the anatomy of the foot of the lacerta gecko, a kind of 
lizard, found in the island of Java, which walks up and down the 
smoothly-polished walls of the Javanese houses, pursuing the 
flies on which it feeds, and it runs upwards to its retreat in the 

How is atmospheric pressure illustrated in the stone-sucker ? 

What facts do marble masons experience connected with the same 
principle? 

What facts in natural history prove the application of atmospheric 
pressure to the position and locomotion of animals? 

What enables flies and other insects to walk upon upright surfaces and 
ceilings ? 

How are the feet of the gecko formed ? 
s 2 



210 PNEUMATICS. 

roof's of houses, though its weight is sometimes 5f ounces. It 
has on each foot five toes, and on the under side of each of these 
are sixteen transverse slits, with serrated edges, and pouches be- 
tween them, by means of which the animal is enabled to form a 
vacuum within the cavities, produced by the application of the 
loose membranes, surrounding the under surface of the toes, to a 
wall or any other smooth plane.* Nature has provided animal 6 ' 
of far superior bulk to this lizard with a similar organization, and 
for the same purpose. 

94. Sir E. Home, from an examination of a specimen of the 
amphibious marine animal, called by naturalists the walrus, from 
the Arctic regions, discovered that there is an analogy in structure 
between the hind foot of the walrus and the foot of the fly; so that 
this large clumsily-shaped animal is enabled to proceed upon the 
smooth surface of ice against gravity, by the adhesion of the feet, 
owing to atmospheric pressure.")" 

95. Those who are but slightly acquainted with natural history 
can hardly be ignorant of the faculty belonging to the fish called 
remora, which fixes itself firmly to the side of a ship or to that 
of a larger fish, as a shark ; and thus it travels without the exer- 
tion of swimming from one part of the ocean to another. It has a 
sort of sucker on its head, by the application of which it becomes 
attached, the pressure of the surrounding water having the same 
effect in this case as that of the air in those previously noticed. 

96. Among the experiments which have been devised to demon- 
strate the elastic pressure and weight of the atmosphere, the fol- 
lowing are well adapted to the purpose. 

i. 

97. Take a quart bottle and drill several holes in the bottom, 
then set it in a wide-mouthed jug, and having filled it quite full 
of water, cork it securely. On lifting it from the jug it will be 
found to hold water notwithstanding the perforations, the pressure 
of the atmosphere preventing its escape ; as will appear on taking 
out the cork, when the water, being equally pressed above and 
below, will run out through the holes till the bottle is emptied. 

ii. 

95. A wine-glass filled with water maybe held with the mouth 
downwards without spilling a drop. The means by which thi9 
seemingly marvellous effect is produced are extremely simple. It 

What advantage does the walrus enjoy in consequence of the peculiar 
tructure of its feet ? 

By what apparatus is the remora enabled to adhere to the sides of a 
vessel or those of a larger fish ? 

In what manner may a vessel, the bottom of whii h is perforated, be 
still made to hold water ? 

* See Abstracts of Papers in Philos. Trans, from 1800 to 1830, vol. ii. 
p. 38. 

t Idem, p>213. 



EXPERIMENTS ON ATMOSPHERIC PRESSURE. 211 

.3 merely necessary to place a piece of paper on the surface of the 
water with which it must be every where in contact, and also 
with the rim of the glass, which is then to be inverted ; and as 
the air cannot get in to act on the liquid above, its pressure is ex- 
erted against the under surface alone. 

in. 

99. A tumbler or goblet may be filled with water, and the 
surface being covered as before with paper, which may be held 
up with the palm of the hand, while it is suddenly inverted, then 
placing it on the surface of a smooth table, the paper is to be with- 
drawn, and the water will remain suspended in the glass; which 
will adhere closely to the table from the pressure of the atmo- 
sphere. Any one may now be safely challenged to lift the glass 
vertically without spilling every drop of the water; for it would 
require some exertion to move the glass at all upwards, and as 
soon as it was elevated on one side, the included water would 
sink down and escape. 

100. It is in consequence of the unrestrained pressure of the at- 
mosphere that liquor will not flow from a cask after it has been 
tapped or pierced, unless another opening be made as a vent-hole 
in the upper part of the cask: for till this is done the force of the 
air pressing on the mouth of the tap, having nothing to counter- 
balance it, would support a column of liquor, if the cask was air- 
tight, the height of which would be proportioned to the specific 
gravity of the liquor. When, however, the air is enabled to act 
through the vent-hole above, the pressure below is counterba- 
lanced, and the liquor descends and runs through the tap by the 
effect fjf its own weight. The operation of the same principle 
may be observed in using a tea-pot ; for there is always a small 
hole in the lid through which the air enters, and without which 
the liquid would not flow from the spout, if the lid fitted close, as 
it ought. 

101. Many circumstances of frequent occurrence may be traced 
to the influence of atmospheric pressure acting irregularly. The 
stoppage of a supply of water from wells and fountains during a 
frost is sometimes owing to this cause ; for the frost does not ex- 
tend far beneath the surface of the earth, but it consolidates it so 
as to prevent the access of air to the channels' of water from which 
fountains and wells are fed, and thus the atmosphere pressing 
only on the open well prevents the water from entering it as usual, 
till a' thaw takes place, and the ground again becoming pervious 
to the air, it acts on the feeding springs, and the water rises in 
the well. 

How is the paradox of the inverted glass of water to be explained ? 

How may a full goblet be inverted upon a table without spilling its con- 
tents ? 

How is atmospheric pressure concerned in the discharge of liquid from 
a cask, urn, or other close vessel ? 

In what manner can you account for the occasional failure of springs 
in severely cold weather ? 




212 PNEUMATICS. 

102. The instrument, called in French Tate-liqueur, 
or Chantepleur, and that used in rilling essence-bottles, 
act on the principle of atmospheric pressure. Their con- 
struction and effect will be readily apprehended from in- 
spection of the annexed figure, which represents a small 
conical tube, A B, open at both ends ; and when in this 
state the lower orifice is plunged beneath the surface of 
any liquid, a portion of it will enter at A, and fill that 
part of the tube A C, which is immersed in the liquid ; 
if then the upper extremity B be closed air-tight by 
placing the thumb over it, the tube maybe lifted out of the liquid, 
and the pressure of the air below will prevent it from escaping, 
till the thumb is removed, and the air thus allowed to act on the 
surface of the liquid at C. The length of the tube to raise water 
in this manner might obviously be extended to more than 30 feet; 
as the height of "the liquid column which the atmosphere would 
keep suspended would be greater or less according to its specific 
gravity. Such instruments of a moderate length are conveniently 
applicable to the purpose of withdrawing a small quantity of any 
liquor through the bung-hole of a cask. 

103. The Siphon* affords another illustration of the principle 
under discussion. It is employed for the purpose of decanting or 
drawing off liquors, and is variously constructed. If an open tube 
of small diameter, bent into the shape of the letter U, be filled with 
water, and the curved side turned upward, the liquid will be sus- 
pended by the pressure of the air on the open extremities, while 
the tube is held in such a position that the columns of liquid in 
both legs shall be exactly of the same height; but if the tube be 
inclined at one side more than the other, so as to destroy the equi- 
librium, the water will run down and escape through that end 
which is at the lowest level. So if a common siphon, or bent 
tube with one side longer than the other be filled with water, and 
inverted or held with the open ends downward, the atmospheric 
pressure acting equally on both sides, and the liquid columns be- 
ing unequal, the water will escape through the longest leg, falling 
in virtue of its own specific gravity. But if, when such a siphon 
is filled, its shortest leg be plunged beneath the surface of water, 
not only will the liquid all run out of the longest leg, but it will 
also rise in the shorter, and be discharged from the other in a con- 
tinued stream, till it sinks below the open end of the shorter leg. 

104. If the siphon be used without previously filling it with 

How may we apply the pressure of air to the purpose of raising small 
quantities of liquor from a cask ? 

To what length might a tube for this purpose be extended ? 

What is the construction and use of the siphon ? 

What principle besides that of atmospheric pressure is concerned in 
producing the continued action of the siphon ? 

Why will not the siphon act without previously filling both legs of the 
tube ? 

* From the Greek r.^v, a tube. 



THE SIPHON. 



213 




the liquid to be decanted, though the liquid will rise in the shorter 
leg, it will not ascend beyond its own level, so as to pass over 
the bend of the tube, and escape, unless the air be drawn out of 
the longer leg. Hence the utility of that kind of siphon repre- 
sented in the margin, the peculiarity of which entirely consists in 
the addition of the tube C, open at the up- 
per end, and communicating below with 
the longer leg of the siphon B. The short- 
er leg A then being plunged into the bung- 
hole of a cask, or into any other vessel 
containing liquor, the opening B is to be 
stopped with the hand, or otherwise, and 
by suction at C, the liquor may be made 
to pass over the bend and fill the leg B, 
when being suffered to escape, it continues 
to flow, as long as the extremity A is im 
mersed in it. Large siphons of this sort, 
made of copper, and furnished with a stop-cock, just above the 
opening B, may often be seen in action ; being used by the dis- 
tillers and liquor-merchants to draw off spirits. 

105. The Wirtemberg Siphon, shown in the following figure, 
when once filled with liquid, will remain so, and hence may be 
hung up in that state ready for use. One leg A being plunged 
into a vessel of the liquid to be drawn off, it will escape through 
the open extremity B, in consequence of the addi- 
tional pressure of the liquid in the vessel at A ; thus 
it will appear that this siphon acts somewhat diffe- 
rently from those of the common construction, though 
it is applicable to similar purposes. 

106. Tantalus's Cup, or the Magical Goblet, is an 
|b *amusing philosophical toy, which consists of a cup 
with a cavity at the sides or bottom, or both, with 
which the longer leg of a siphon communicates ; so that when 
water is poured into the cup high enough to overcome the pres- 
sure of the air on the end opening into the cavity, the liquid will 
sink in the cup, and run into the cavity; and thus it can never 
rise so high as the mouth of the figure within which the siphon is 
concealed ; and the classical fable of Tantalus is realized. There 
must be an aperture near the rim of the cup to admit air into the 
cavity, or rather to suffer it to escape, and by closing it with the 
finger, the cup may be filled to the brim ; but as soon as it is un- 
closed the water will sink as before. If a hollow handle, com- 
municating with the lateral cavity, be fitted to the cup, the hole 
may be so placed at the Inner side of the handle as to escape no- 
tice ; and the effect will appear astonishing to those unacquainted 
with the theory of atmospheric pressure. 



To what practical purpose is the siphon frequently applied ? 
What advantage is possessed by the Wirtemherg siphon ? 
In what manner is the cup of Tantalus constructed ? 



214 PNEUMATICS. 

107. Intermitting fountains, or periodical springs, are found in 
some places, and from the capricious and apparently unaccounta- 
ble irregularity of such streams they have been regarded as mira- 
culous, in dark ages, and have given rise to abundance of super- 
stitions among the common people. There is a remarkable spring 
of this kind called Lay well, near Torbay, in Devonshire, England, 
and the peculiarity of this and other intermitting fountains, may 
be satisfactorily shown to arise from the operation of siphons 
formed by nature, communicating with subterraneous reser- 
voirs.* 

108. The siphon may be made available for the purpose of con- 
veying water over the side of a pond or reservoir into another, 
provided the latter is on the same or a lower level than the form- 
er. It was thus very ingeniously applied by a French engineer, 
M. Garipuy, in 177(J, to discharge the surplus quantity of water 
from the canal of Languedoc, when it had been raised above the 
proper level by the influx of water at the mouth of the river Ga- 
ronne during a storm. 

109. Whenever water is conveyed by pipes from a higher to a 
lower level, over an intervening eminence, the principle on which 
the e,iphon acts must be adopted ; and thus water may be made to 
pass over any height not much exceeding 30 feet. It is thus con- 
ducted from Lochend to Leith, near Edinburgh, through pipes, 
the intermediate ground being 8 or 10 feet above the fountain head. 
It is necessary that the water should be driven in the first instance 
beyond the most elevated part of the pipe by a forcing-pump, and 
it then continues to flow by the influence of atmospheric pressure. 
But as air, always loosely combined with flowing water, will 
be gradually extricated from it at the bend or highest part of the 
pipe, it will at length there accumulate so as to stop the flux of 
the water. When this happens, the forcing-pump must be worked 
to renew the current. 

110. From what has been stated with regard to the siphon, it 
follows that it can only be used for transferring liquids from higher 
to lower levels ; therefore when water or any other liquid is to be 
raised by means of atmospheric pressure, some kind of pump 
must be employed. Pumps are variously constructed. The mar- 
ginal figure below, (111,) represents the common suction pump, 
which is nothing more than a syringe so contrived that the water 



With what natural phenomena are the principles of the siphon con- 
nected ? 

From what source do intermitting springs derive their supply of water ? 

For what hydraulic operations may the siphon be employed? 

How high may water be made to pass over a barrier ? 

In what manner is the siphon trunk for such purposes usually filled ? 

* For an account of Lay well, see Philos. Trans., No. 424; see also Nos. 
119, 189, 192, and 384. There is an interesting paper on the noted inter- 
mitting spring at Giggleswick, in Yorkshire, by Mr. Gough, of Kendal, in 
Nicholson's Journal of Natural Philosophy, 8vo. 



THE SZ CTION-PUMP. 



215 



drawn into it passes through the piston by means of a valve, and 
is discharged above it, instead of being again forced out below 
The invention of this instrument is attributed by Vitruvius to 
Otesibius or Ctesebes, an Athenian engineer, who lived at Alexan- 
dria, in Egypt, about the middle of the second century before the 
Christian era; and the construction of syringes, fire-engines, and 
other machines acting on similar principles is described by his 
scholar Hero, in a treatise on Pneumatics, still extant. 

111. The suction-pump consists q{' 
two hollow cylindric pipes A and E, 
the latter of which usually terminates 
below in a perforated ball, through 
which the water in the well enters 
freely into the suction-pipe; and at 
its other extremity is a valve D, open- 
ing upwards, and affording a com- 
munication, when open, with the up- 
per pipe A. In this pipe, constituting 
the barrel or body of the pu i p, the 
piston B moves air-tight vertically, 
and by its valve C opening upwards, 
it permits the water to pass above it 
and be discharged at the spout. Now 
suppose the piston to be at the bot- 
tom of the barrel in contact with the 
valve D, on lifting the former by do- 
pressing the lever handle of the pump, connected with the piston- 
rod at F, the valve C will be closed by the pressure of the air 
above, and a vacuum being thus formed in the barrel, the same 
pressure on the surface of the water in the well, will drive it up 
the suction-pipe, and raising the valve D, the water will enter the 
exhausted barrel, whence by depressing the piston, the valve D 
will be shut, and that at B rising, the water will pass upwards and 
be discharged through the spout. The first effect of working 
such a pump must be to form a partial vacuum in the barrel of the 
pump, and the upper part of the pipe E, and it will be only after 
the whole of the included air has been expelled through the pis- 
ton-valve, and replaced by water in the pipes, that the liquid be- 
gins to flow, the atmospheric pressure below taking full effect, 
while the equivalent pressure above is counteracted by the manual 
force applied to the handle of the pump. 

112. The suction-pump cannot raise water beyond the extent of 
action of atmospheric pressure, the utmost limit of which will be 
about 34 feet; so that the height of the valve D above the level 

Describe the construction and operation of the common pump. 

To whom is its invention attributed ? 

By wbom were syringes and fire-engines first described ? 

What closes the upper valve of the suction pump before it has become 
immersed in water ? 

What is the first operation which takes place within the barrel of the 
pump ? 




216 



TNEUMATICS. 



of the water in the well must never exceed that distance ; and 
unless the pump be accurately constructed, so that the piston in 
its descent fits close to the bottom of the barrel, so as to form a 
perfect vacuum in its ascent, the water will not rise to the ex- 
treme height in the suction-pump. It must appear somewhat 
paradoxical, that though this will be the effect when the pump is 
in the best working order, the valves and pipes being air-tight, 
yet a pump, the suction-pipe of which has been damaged, so that 
a small quantity of air can enter, will raise water nearly as high 
again as a good pump. 

113. A tinman of Seville, in Spain, ignorant of the principles of 
science, undertook to construct a suction-pump to raise water from 
a well 60 feet deep : when the machine was finished, he was con- 
founded at discovering that it had no power to raise water at all, 
and enraged at his disappointment, while some one was working 
the pump he struck the suction-pipe with a hammer or axe, so 
forcibly as to crack it, when to his surprise and delight the water 
almost immediately began to flow, and he found that he had thus 
attained his purpose. This happened about 1766, when M. Le- 
cat, a celebrated surgeon, then at Rouen, in Normandy, being in- 
formed of it, made a similar experiment on a pump in his garden, 
b)^ boring a small hole in the suction-pipe, 10 feet above the level 
of the water in the cistern, and having adapted to it a stop-cock, 
he found that when it was open the water could be discharged at 
the height of 55 feet, instead of from 30 to 34 as before.* The 
circumstance admits of an obvious explanation, the effect being 
analogous to that exhibited by jefs-cPeau, when air is mingled 
with the acending column of liquid. f Thus in the case of the 
pump, the air presses in through the slit or aperture in the suc- 
tion-pipe, and becoming mixed with the water in its ascent, forms 
a compound fluid, far lighter than water alone, and therefore acted 
upon by atmospheric pressure more 
readily, and thus it produces the phe- 
nomenon described. However, as 
there are other and more efficacious 
methods of raising water to great 
heights, the contrivance just noticed 
is not to be recommended. 

114. The Lifting-pump, as repre- 
sented in the margin, acts in much 
the same manner as the preceding, 
but the machinery is reversed. It 
consists of a hollow cylinder or barrel 
A B, in which is fixed the valve G, a 
little below the level of the water in 
the well or reservoir. A piston F 
with a valve opening upwards, fits 
into the lower part of the barrel, in 

* V. Si?iuid de la Fond Elem. de Pbys., t. iii. pp. 238, 239. 
f See Hydraulics, No. 11. 




FORCING-PUMP. 



217 



which it is movea vertically by means of the frame BCDE, con- 
nected with the piston-rod I. Now when the piston is at the bot- 
tom of the barrel, the pressure of the atmosphere on the surface 
of the w T ater in the well will open the piston valve ; and the wa- 
ter will rise to the same height within the barrel as without; and 
on lifting the piston, its valve F will close, and the water above 
it will be driven by the opening of the valve G, into the upper 
part of the barrel: then the piston being depressed again, the 
valve F will open to admit more water into the lower part of the 
barrel, while that above will be prevented from returning by the 
closing of the valve G ; and thus by continued working of the 
piston, the water will rise in the barrel till it escapes by the spout. 
115. In both the suction-pump and the lifting-pump, the water 
will be discharged by jets, unless a kind of reservoir is made by 
ihe enlargement of the barrel above the spout, in which case it 
may be made to flow in a continuous stream. 

116. The forcing-pump is another form of this use- 
ful machine, combining in a great degree the proper- 
ties of those already described. It is composed of a 
hollow cylinder, the lower end of which dips into the 
water in the well; just above the valve, in the upper 
part of this cylinder, a lateral pipe branches off, hav- 
ing at a short distance from its origin another valve, 
both valves opening upwards ; and in the upper part 
of the cylinder or barrel is a solid piston or plunger, 
moving air-tight vertically. Now if the piston be 
depressed to the lower valve, and then raised, that 
will open, while the valve in the lateral pipe remains 
closed, and the pressure of the atmosphere on the 
water in the well will cause it to rise a little and ex- 
pel a part of the air through the first valve ; the pis- 
ton then being lowered that valve will close, and 
the air above it be expelled through the other valve ; thus every 
elevation of the piston will make the water rise higher in the cy- 
linder t 1 ! it has expelled all the air, and it will consequently, at. 
the nexi lifting of the piston, pass above the first valve, and the 
piston oeing again lowered, as the liquid cannot descend, the 
valve being closed, it will be forced into the lateral pipe, through 
its valve, and as it is prevented from returning again by that valve, 

What is the greatest height to which water may be drawn up by a well 
constructed pump of this form ? 

In what manner was it discovered that a mixture of air and water may, 
by the action of a pump, be raised higher than 34 feet ? 

How is this action explained ? 

Of what does the lifting-pump consist ? 

Is the lifting-pump limited to any particular height to which it can 
raise the liquid column ? 

In what manner is a constant stream maintained either in the lifting or 
*he suction-pump ? 

Describe the form and action of the forcing-pump. 

Which of the preceding pumps constitutes a part of this ? 




218 AEROSTATICS. 

it will continue to ascend with every down-stroke of the piston, 
and may thus be raised to any height required 

117. In a pump of this kind, the stream will be intermitting 1 , 
unless there be a cistern above the spout, to form a head of water 
which may act by hydrostatic pressure ; or the same object may 
be more effectually attained by closing the force-pipe, so that a 
portion of condensed air may press on the surface of the water 
after it has passed the valve, and an open tube, fitting air-tight, 
entering the chamber, and having its lower extremity, plunged be- 
neath the surface of the water, that liquid will be driven up it by 
the pressure of the included air, and form ajet-d'eau, or flow in a 
regular stream, according to the disposition of the spout or mouth- 
piece. 

118. The fire-engine is a modification of the forcing-pump, con- 
sisting essentially of two working barrels, like an air-pump, but 
fitted with solid pistons, and valves corresponding with those of 
the forcing-pump ; and thus water is drawn from any reservoir or 
other source of supply, and propelled into a strong air-chamber, 
from the upper part of which passes a tube, having its inferior ex- 
tremity dipped under the surface of the water, which is thus 
driven through it by the pressure of the condensed air. The tube 
just mentioned may be connected with the part that enters the 
air-chamber by a universal joint, and thus its extremity may be 
conveniently turned to throw water in any direction ; or as more 
usual, it may have fitted to it a flexible leathern pipe or hose, by 
means of which the stream may be conducted to any spot where 
it may be made to act with the greatest effect. 



AEROSTATICS. 



119. The laws which regulate the ascent and descent of floating 
bodies have been generally elucidated in treating of specific gra- 
vity, as connected with the science of Hydrostatics. It was there 
demonstrated that liquids differing in density when placed in con- 
tact would assume an arrangement depending on their relative 
weights or densities, the heaviest always sinking to the bottom of 
the containing vessel, and the others floating at heights corres- 
ponding to those weights.* Solids, immersed in liquids, in the 
same manner either sink or float according as they may be heavier 
or lighter than the medium in which they are placed. Thus if a 
vessel were partly filled with mercury, and water standing above 

What device maintains a constant efflux in the forcing-pump ? 
What are the essential parts of the fire-engine ? 

What device enahles the fireman to direct the stream in any direction, 
according to circumstances ? 

* See Hydrostatics, No. 76. 



OF FECUNDATION. 219 

it, then on dropping into it a piece of iron, the solid metal would 
be seen to fall through the upper stratum of the liquid mass, and 
stop at the surface of the lower stratum, as consisting- of a metallic 
fluid more dense than the solid metal. 

120. An analogous effect might be exhibited with gases of dif- 
ferent densities. If a quantity of carbonic acid or fixed air were 
to be poured into a large glass jar, so as to fill the lower half of 
it, the upper part of the jar would be occupied by atmospheric air, 
as the lighter of the two fluids ; and any bodies of specific gravity v 
intermediate to these gases, as soap bubbles, being let loose over 
the jar would fall through the upper stratum of gas, and be ar- 
rested by the lower, on the surface of which they would float, just 
as a cork would float on water. 

121. A great number of substances of various kinds are sus- 
pended in the atmosphere within a moderate distance from the 
surface of the earth ; some of them, in consequence of their ex- 
treme minuteness, belonging to the class so picturesquely de- 
scribed by Shakspeare as "the motes that people the sunbeam." 
These floating corpuscules appear to be numerous in proportion to 
the heat of the air ; and hence they are much less frequent in win- 
ter than in summer. 

122. "We are ignorant of the precise nature of this fine pow- 
der. Perhaps it may be a mixture of inert matter extremely 
divided, with the exquisitely small germs of various species of 
organized bodies, as the eggs of insects, the seeds of plants, and 
likewise the fecundating powder from the stamens of flowers. It 
is in fact known from the observations of naturalists, that under 
many circumstances, animalcules and minute vegetables of dif- 
ferent species become developed, though it is impossible to per- 
ceive the germs from which they are derived. It is certain, also, 
that flowers furnished with pistils only, (as those of the date 
palm,) are fecundated, and bear fruit, though the plants furnished 
with stamens are found at considerable distances, and even sepa- 
rated from the others by vast tracts of sea. All these observations 
tend to confirm the hypothesis of the transmission of germs and 
fecundating powders by means of the atmosphere. Indeed we 
take nature in the fact, as it were, under many circumstances ; 
thus plumose or tufted seeds are frequently observed flying in the 
air, as those of the lettuce, the dandelion, and others, with which 
children sometimes amuse themselves. And it may be perceived 
that the seeds of many species of vegetables are furnished with 
delicate membranes or wings ; as, for instance, those of the fir 

What analogy exists between the phenomena of liquids and those of 
gases, when different kinds are poured Into the same vessel ? 

Give examples of that analogy. 

In what manner is the floating dust of the atmosphere seen in warm 
sunny weather to be accounted for ? 

Is the ascension of those substances trom the earth rendered probable 
Dy any known facts in natural history ? 

What seems to be the design of the thin membranes and delicate gos- 
samer with which the seeds of certain plants are furnished ? 



220 AEROSTATICS. 

the elm, &c, which seem formed expressly in order that the wind 
may raise them, so that they may be transported in all directions, 
and thus contribnte to the propagation of the species to which they 
oolong 1 . 

123. " Relatively to the fecundating powders, it may be re- 
remarked, that in forests of pines and firs, at the period of flower 
ing, the ground is covered for several days with an extremely fine 
light powder, which becomes raised in the air by the winds in 
prodigious quantities, and conveyed to distant places, where tha 
descending clouds have been often mistaken for showers of sul- 
phur. Also during the season of the flowering of wheat, the fe- 
cundating dust, or pollen, may be seen floating over the fields 
like a thick mist."* 

124. The modern art of aerostation, or as it has been more cor- 
rectly styled aeronautics, depends on the application of the prin- 
ciple of specific gravity to the action of gases on solid bodies, and 
the consequent motion of the latter through the atmosphere. 
After the invention of the air-pump, when the mechanical proper- 
ties of the air had been experimentally demonstrated, the feasi- 
bility of contriving a machine for the purpose of navigating the 
atmospheric regions became a favourite subject of speculation 
among men of science. 

125. Bishop Wilkins, a distinguished mathematician, and one 
of the earliest members of the Royal Society of London, was so 
far convinced that a method of travelling through the air might 
be discovered, that he hazarded the opinion that the time would 
come when a man about to take a journey would call for his wings 
as familiarly as he might now for his boots. But the idea of taking 
advantage of the principle of specific gravity to form a flying-engine, 
that should rise in consequence of its being lighter than an equal 
bulk of air, appears to have been first published, if not conceived, 
by Francis Lana, an ingenious Jesuit. The scheme lie proposed 
was that of attaching to a car four hollow globes of copper, which 
were to be exhausted by means of an air-pump ; and which he 
imagined would have sufficient ascending power to elevate the 
car and the aeronautic adventurer. It seems to have been merely 
a theoretical project, which must have failed in the attempt to ex- 
ecute it ; for neither globes of copper nor any other substance 
known could be manufactured in such a manner as to be at once 
buoyant, from the thinness of the sides, and strong enough to re 
sist atmospheric pressure. 

What remarkable appearance is often exhibited by the surface of t 
earth in the flowering season of pines, firs, &c. ? 

How early, and by what occurrences, were men induced to attempt t.i 
rial navigation ? 

What appears to have been the earliest conception of this subject,- and 
jiow did it differ from the idea of Lana ? 

Why was the project of the latter impracticable ? 



* Beudant Traite Elem. de Physique, y\ . S£ , 335. 



THE AIR-BALLOON. 221 

126. Nearly a century had elapsed after the publication of the 
abortive plan just noticed, when the discovery of hydrogen gas, 
or inflammable air, by Cavendish, about 1766, and of its remarka- 
ble inferiority of density compared with common air, revived the 
speculations of philosophers on the subject of aeronautics. Dr. 
Black, of Edinburgh, soon after ascertained, by experiment, that 
a thin bladder filled with hydrogen gas would rise to the ceiling 
of a lofty room, and remain suspended till it was taken down ; and 
several years subsequently the subject was farther investigated 
by Cavallo, a Portuguese gentleman, residing in England, who 
was a fellow of the Royal Society. 

127. It was, however, in France that the invention of the air- 
balloon took place. Two brothers, Joseph and Stephen Montgol- 
fier, paper-makers, at Annonay, constructed a large square bag of 
fine silk, and caused it to ascend in an inclosed chamber, and af- 
terwards in the open air, by heating the air within it by means of 
burning paper. After several preliminary experiments, a balloon 
was constructed at Paris, consisting of an elliptical bag, 74 feet 
in length, and 48 in breadth, with an aperture below, near which 
was suspended an iron grate for burning wood and straw, and a 
boat or car attached for the reception of aerial travellers ; and in 
this machine the first ascent was made, in October, 1783, by Pila- 
tre de Rozier, superintendent of the Royal Museum. Other ex- 
periments of the same kind followed, with balloons rendered buoy- 
ant by the admission of heated air. 

128. But this method of aerostation was liable to inconveni- 
ences and imperfections, which rendered it less eligible than that 
of employing balloons inflated with hydrogen gas, the chief ob- 
jection to which arose from the expense attending it. This, how- 
ever, was obviated by means of a public subscription ; and De- 
cember 1, 1783, M. Charles, professor of natural philosophy, at 
Paris, and his companion M. Robert, ascended from the gardens 
of the Tuilleries, by means of a balloon filled with hydrogen or in- 
flammable air. The success of this undertaking demonstrated 
the superiority of this mode of construction ; and it was conse- 
quently adopted by many other experimentalists, both in France 
and elsewhere. Lunardi, an Italian, was the first aeronaut who 
exhibited in England ; and among those who distinguished them- 
selves by their enterprising spirit, or philosophical researches, 
amidst the fields of air, may be noticed the names of Blanchard, 
Garnerin, Zambeccari, Dr. Jeffries, W. Windham Sadler, ami 
Gay-Lussac, the last-mentioned of whom, in 1804, ascended from 

How long was Lana's scheme published before the discovery of hydro- 
gen gas ? 

What experiment by Dr. Black is probably the earliest form of balloon 
ascension ? 

In what manner did the Montgolfiers effect the elevation of their silk bag? 

What is related of the form and size of the first balloon with which an 
aeronautic expedition was made by Rozier ? 

Why was not hydrogen adopted by the earliest aeronauts ? 

Who were among that number . ? 

t 2 



222 AHROSTATICS. 

Paris, furnished with instruments for making meteorological ob- 
servations; and from the descent of the mercury in his barometer, 
he inferred that he had, when at his utmost elevation, attained the 
height of about 23,000 feet above the level of Paris; and this ap- 
pears to be the greatest distance from the surface of the earth to 
which any person has hitherto risen by means of an air-balloon. 

129. Several accidents have occurred to aeronauts in the prose- 
cutions of their adventures, and some have lost their lives ; as 
Pilatre de Rozier, who, after repeated successful ascents, was 
killed, together with M. Romain, in consequence of the balloon tak- 
ing fire in which they had attempted to pass from France to Eng- 
land, in June, 1785 ; Madame sBlanchard, the wife of the aeronaut, 
mentioned above ; and W. W. Sadler, who, after having made 
thirty atmospheric voyages, in one of which he crossed the Irish 
Channel, was precipitated from his balloon, owing to the car 
striking against a chimney, at the height of about forty yards 
from the- earth. Notwithstanding these and other fatal disasters, 
aeronautic expeditions have been so frequently undertaken, that 
most persons must have had opportunities for witnessing them ; 
but though several useful purposes to which air-balloons might be 
applied have been suggested, the difficulty of managing them has 
hitherto prevented their adoption except as objects of display. 

130. The air-balloon consists of a light bag of thin silk, of a 
globular or elliptic shape, and rendered air-tight by a coating of 
varnish, made by dissolving gum-elastic in spirits of turpentine. 
When thus prepared, it must be distended with some elastic fluid, 
lighter than common air ; and it will thence acquire an ascending 
power equal to the difference between its weight, including the 
attached car and its contents, and that of the bulk of atmospheric 
air which it displaces. Suppose the diameter of the silk globe 
to be 20 feet, its circumference will be about 63 feet, its superfi- 
cial measure about 1257 square feet, and its contents, solid mea- 
sure, 4190 cubic feet; then if it be filled with gas having only 4 
of the specific gravity of common air, and admitting that a cubic 
foot of the latter would weigh 1| oz., and that 1 square foot of 
taffeta or thin silk would weigh 1 oz.: — 

The weight of atmospheric air displaced will be 6285 oz . 



The weight of gas in the balloon - - - 1571 £ 
The weight of the taffeta - - - - 1257 



2828* 

3456# 

To what height did Gay-Lussac ascend ? 

To what purpose have balloons been hitherto applied ? 

Of what does the air-balloon consist ? 

What would be the ascensional force of an unloaded balloon of silk 20 
feet in diameter filled with hydrogen of a specific gravity £ that of com- 
mon air? Calculate on similar principles the force of a balloon 30 feet 
n diameter } 



THE PARACHUTE. 223 

131. Hence the inflated balloon would weigh 3456 oz., or 216 
pounds less than an equal bulk of common air ; and therefore such 
a balloon, with a car and its contents attached, weighing- 200 
pounds, would have an ascending force equal to 16 pounds. But 
if it were filled with pure hydrogen gas, having a specific gravity 
but 1-13 that of common air, its power of ascension would mani- 
festly be augmented in a high degree. 

132. Aeronauts in general were accustomed to use inflammable 
air, procured by dissolving pieces of iron or zinc in sulphuric acid 
diluted with water ; a tedious, troublesome, and inconvenient 
operation, which was never found to produce gas approaching to 
the specific gravity just mentioned. Hence Mr. Green, who has 
distinguished himself by the number of his aerial expeditions, 
amounting to about one hundred, determined to make a trial of coal 
gas. From some preliminary experiments he ascertained that the 
ascending force of a balloon three feet in diameter, when inflated 
with gas from coal, was equal to 11 oz. ; and that when filled 
with hydrogen gas procured in the usual way, its force was not 
more than 15 oz. He therefore, in his ascents in the neighbour- 
hood of London, availed himself of the convenience of procuring 
gas from the coal-gas companies, which he found to be sufficiently 
adapted for his purpose. 

133. The accidents which occurred to some of the earlier aero- 
nauts suggested the idea of contriving a method of descending 
independent of the balloon, if circumstances should render it desir- 
able. The first experiments for this purpose were made by Le 
Normand, in 1783 ; and Blanchard subsequently constructed a 
machine resembling a large expanded umbrella, called a para- 
chute, which he let fall from a height of 6000 feet above the earth, 
with a dog in a basket suspended from it. A whirlwind arrested 
its descent and swept it above the clouds; but it soon approached 
the balloon again, when the dog recognized his master, showing 
nis uneasiness and alarm by barking; another current of air then 
carried him out of sight, and he ultimately landed in safety, though 
not till after the descent of the balloon. Garnerin, who used" a 
parachute 25 feet in diameter, with a basket attached to it, descend- 
ed from the air by this means, several times, both in France and 
in England; and on one occasion from the perpendicular eleva- 
tion of 8000 feet. 

134. On the principle of the parachute depends the buoyancy 
of numerous light bodies presenting an extended surface to the 
air ; and thus a little canopy made by attaching four strings to the 
angles of a sheet of paper with a light weight in the place°of a car, 
if dropped from an eminence will descend but slowly to the ground. 

What has recently been substituted for hydrogen in the inflation of 
balloons ? 

What relative ascensional forces will be given to balloons by coal-gas 
and hydrogen respectively ? 

What is the form and what the object of the parachute ? 

What accounts are given of the use of this apparatus * 



224 AEROSTATICS. 

Some experiments founded on the observation of such facts, made 
in Germany, may here be noticed. Zacharia of Rosleben, conceiv- 
ing the possibility of forming a flying boat, constructed, by way 
of trial, a case of light wood covered with linen, in the shape 
of a flat obtuse-angled keel, 5| feet in diameter, and i a foot deep, 
weighing 14i pounds. On the 17th of September, 1822, this ma- 
chine was launched from a scaffold on the race-course of Wen- 
delstein, the scaffold being 27 feet high, and standing on a rock 
100 feet above the surrounding plain; so that the perpen- 
dicular height was 127 feet; and the boat flew to the distance 
of 153 feet. A second flying boat 7i feet in diameter, % a foot 
deep, and 25 pounds in weight, which was launched from the 
scaffold on the same day, took a somewhat more elevated path, and 
landed after a flight of 158 feet. These experiments appear to 
have been expensive, and the result was not sufficiently flattering 
to induce the projector to repeat them.* 

135. Attempts have been made at different periods to construct 
wings for active flight through the air ; but they have all proved 
abortive. The celebrated historian, William of Malmesbury, in 
his account of the conquest of England by the Normans, men- 
tions an alleged prediction of that event, by Elmer, or Oliver, a 
Benedictine monk of Malmesbury, in consequence of the appear- 
ance of a comet, in 1060. This monk appears to have been a 
learned and ingenious man, who was skilled in mathematics. 
But his claim to notice at present is grounded on his being the 
earliest English aeronaut on record ; though his speculation was 
not only unsuccessful but unfortunate. For the historian informs 
us that Elmer, having affixed wings to his hands and his feet, as- 
cended a lofty tower, whence he took his flight, and was borne 
upon the air for the space of a furlong ; but owing to the violence 
of the wind or his own mismanagement through fright, he fell to 
the ground, and broke both his legs.f 

136. The famous Roger Bacon, who died towards the end of 
the thirteenth century, in his treatise on the Secret Works of Na- 
ture and Art, expressly asserts the possibility of constructing 
machines in which a man sitting might move through the air, by 
means of wings, like a bird frying.:}: In the fifteenth century, 

What success has attended the various attempts which have been made 
to employ aerial boats ? 

How early do attempts of this kind appear to have engaged the serious 
attention of speculative men r 

Wbat success attended the flights of Elmer, Dante, and Degen ? 

* Elements of Natural Philosophy. By Prof. Vieth, of Anhalt-Des- 
sau, (German.) Leipsic, 1823. p. 208. 

t Gul. Malmesbur. de Gestis Regum Anglorum, lib. ii. cap. 13. 

^ " Possunt etiam fieri instruments volandi ut homo, sedens in medio 
instrument^ revolvens aliquod ingenium, per quod alse artificialiter com- 
posite aerem verberent, ad modum avis volantis." — Epistola Fratris R. 
Raconis de Secretis Operibus Nature et Artis. Hamburg. 1572. p. 37. 



THE SKY-ROCKET. 225 

John Baptist Dante, a mathematician of Perugia in Italy, excited 
the astonishment of his contemporaries by his aeronautic exploits. 
But his career was unfortunate ; for we are told that after he had 
repeatedly crossed the lake of Thrasymene through the air, he 
took his flight from an eminence in his native city, when his ma- 
chinery becoming deranged, he fell on the roof of a church, and 
fractured his thigh. The Journal des Sgavans, December 12, 1678, 
contains a description of a flying-engine contrived by a locksmith 
of Sable, in the county of Maine, in France, by means of which 
the inventor descended from a second floor window, and proposed 
to fly from a height over a river. Professor Vieth says, that the 
latest experiments on the art of flying were made by a watch- 
maker at Vienna, named Degen ; but they seem to have led to no 
practical results of importance.* 

137. The ascent of sky-rockets affords an interesting object of 
philosophical speculation, and the phenomenon has been variously 
accounted for by men of science. The rocket consists of a cy- 
lindrical case or cartouch of thick paper filled with a composition 
of gunpowder, charcoal, steel filings, and other inflammable mat- 
ter; with a head technically styled " tbe pot," at the upper ex- 
tremity ; and a light stick, to which the rocket is affixed laterally. 
Its flight, like that of other projectiles, depends on the sudden expan- 
sion of compressed air, formed by combustion. The cause of the 
ascent of the rocket is, that whereas it would, if it were not for the 
aperture below, be equally pressed on all sides within by the ex- 
panding gas, and would remain at rest, but this pressure, like that 
of steam in a boiler, will often on a small portion of its inner sur- 
face greatly exceed the weight of the containing vessel. In such 
cases, the opening of an aperture sufficiently large, will project the 
container in the direction opposite to that in which the opening 
takes place. It will be perceived that from this account of the effect, 
the operation would be the same in vacuo as in the open air. In 
fact the effect is no more due to the impinging of the escaping gas 
against the air below, as Dr. Hutton and others have supposed, 
than the effect of effluent water in Barker's mill is to be attributed 
to the same cause. Several steam-boilers which have exploded 
in the United States have gone off through the air like rockets, 
having first formed a rent in such a part as to allow the issuing 
steam to urge the enormous mass forward by its elastic action. 
One occurrence of this kind at Pittsburg was, at the time, de 
scribed as having been accompanied by a train of light ; as if the 
issuing stream had been an inflammable mixture. A revolving 

Of what does the sky-rocket consist ? 

On what does its flight depend ? 

What causes the rocket to ascend when the contents are inflamed ? 

What analogous effects on a larger scale have sometimes been wit- 
nessed ? 

By what method is the rapid developement of gases obtained in the 
rocket } 

* Elem. of Nat. Philos., p. 209. 



226 AEROSTATICS. 

apparatus, like a Barker's mill, only adapted to the action of air 
instead of water, may be set in motion by condensed air ; but will 
revolve with rather more velocity if placed in the receiver 
of an air-pump, and, after exhaustion, set in motion by allowing 
the external air to find an entrance through the revolving arms. 
Dr. Hutton justly remarks that the rocket would not rise unless 
the elastic fluid were produced in abundance ; and hence the 
necessity for piercing in the centre of the rocket a conical hole, 
and thus the composition when inflamed burns in concentric strata, 
of much greater extent than the circular disk to which the com- 
bustion must otherwise be confined, and the expansive gas is 
formed in quantities sufficient to produce the required effect. 

138. Among the amusements of schoolboys there are few more 
susceptible of application to useful or curious purposes than that 
of flying paper-kites. By means of such a machine, which he 
constructed by stretching a silk handkerchief over a wooden frame, 
Dr. Franklin demonstrated the identity of lightning with the 
electric fluid;* the paper-kite has been employed to convey a line 
to the shore from a vessel wrecked on a rocky coast ;f and a few 
years ago, a Mr. Pocock, of London, made repeated experiments, 
by means of which he ascertained the possibility of travelling in 
a carriage drawn by two paper-kites, supported at a moderate ele- 
vation, and impelled by the wind. The elevation of the paper- 
kite in the usual manner, with a line attached to a loop on the 
under-side of the machine, is satisfactorily elucidated by Dr. Pa- 
ris, who has shown that the ascent of the kite affords an example 
of the composition of forces, the mode of action of which is exhi- 
bited in the following diagram. 




139. The kite is here represented rising from the ground, the 
line W denoting the direction and force of the wind, which falling 
on an oblique surface, will be resolved into two forces, namely, 

To what useful purposes has the kite been occasionally converted ? 
On what principle is its ascent to be explained ? 

* See Treatise on Electricity. 

f See Transactions of the London Society for the Encouragement of 
Arts, Manufactures, and Commerce, vol.xii. 



THE DIVING-BELL. 227 

one parallel with it, and another perpendicular to that surface, and 
the latter only, represented by the line Y, will produce an effect, 
impelling the kite in the direction O A ; and the tension of the 
string, at the same time, in the direction P T S, Avill cause the 
machine to ascend in the diagonal O B of the parallelogram A 
B T.* The ascent of the paper-kite not only depends, as may 
be thus perceived, on the same principles as those which govern the 
movement of bodies on inclined planes ; but it may also be fairly 
affirmed that the path of the kite in rising is an actual inclined 
plane, up which it is drawn, by the tension and weight of the 
string. 

140. A well constructed kite may be made to ascend when 
there is little or no wind stirring ; for, by running with it held by 
the string and inclined obliquely, the air on its inferior surface will 
be compressed, just as it would be by running with an expanded 
umbrella held out ; and by veering out the string and running at 
the same time, the kite is drawn up an inclined plane which it 
forms for itself by the gradual compression of the successive por- 
tions of air over which it moves. 

The Diving-bell. 

141. As air produces peculiar effects when its density is inferior 
to that of the lower atmosphere, so likewise are certain effects 
produced by air, the density of which has been augmented by 
compression or otherwise. Condensed air, if not contaminated 
w T ith deleterious gases, may be breathed with impunity by ani- 
mals for a considerable time ; though its effects are various on dif- 
ferent individuals, and some experience considerable temporary 
inconvenience from inspiring it. Mr. Bille, of New York, has 
founded on this property of compressed air an improved method 
of bottling sparkling liquids, such as ale, cider, and perry. His 
plan consists in conducting the whole operation of drawing off, 
bottling, corking, and securing the liquors in question, within an 
air-tight chamber, into which such a quantity of air may be com- 
pressed by a condensing pump or engine, that it may always 
afford a degree of pressure on the surfaces of the liquors sufficient 
to prevent the escape of the gas to which they owe their sparkling 
quality. 

142. But the most interesting and important purpose to which 
the respirability of compressed air has been applied, is that of en- 
abling persons to descend to a certain depth beneath the surface 
of the sea, by means of the machine called a diving-bell. The 

What path does it actually describe in rising ? 
How may the kite be made to rise in a calm ? 
How is the ascent in this case produced ? 

What effect on the respiration of animals is produced by air above the 
common density ? 

What application of such air has been made to purposes in the arts ? 

* Philosophy in Sport made Science in Earnest. New edit. 1833, p 236. 



228 AEROSTATICS. 

compressibility and impenetrability of atmospheric air may be 
both at once demonstrated by the simple experiment of holding 
by the foot an inverted beer-glass, and plunging it perpendicularly 
in a jar or basin of water, when the portion of air within the beer- 
glass will be compressed and diminished in bulk, in propor- 
tion to the depth to which the glass was pressed beneath the sur- 
face of the water : but a limit would occur beyond which manual 
force would not drive it. If a small bit of lighted wax-taper, 
attached to a cork, were placed on the water and included under 
the inverted glass, it would burn in the compressed air longer 
than in an equal bulk of air at its usual density; but the air would 
be consumed by the combustion of the taper till it became reduced 
to about one-third, and the residue would be found unfit for respi- 
ration and the support of animal life. 

143. A diving-bell is merely a large conical or pyramidal ves- 
sel, made of cast iron, or of wood, the latter loaded with weights 
to make it sink. It is usually furnished with shelves and seats 
on the sides for the convenience of those who descend in it ; and 
several strong glass lenses are fitted into the upper part for the 
admission of light. There is likewise a stop-cock, by opening 
which the air, rendered impure by respiration, may from time to 
time be discharged and rise in bubbles to the surface of the wa- 
ter ; and provision must be made for the regular supply of fresh 
air, which may be sent down through pipes from one or more 
large condensing syringes, worked on the deck of a vessel above. 
The bell must be properly suspended from a crane, or cross-beam, 
furnished with tackles of pulleys, that it may be lowered, raised, 
or otherwise moved, according to circumstances. 

144. Some have supposed that the ancients were acquainted 
with the use of the diving-bell, and apparent allusions to it occur 
in the works of Aristotle. But the earliest direct notice of such 
a machine is probably to be found in a tract "De Motu Celerri- 
mo," by John Taisnier, who held an office in the household of the 
emperor Charles V. He states that some experiments were madj 
in the presence of that prince, at Toledo, in 1538, by two Greeks, 
who descended under water several times in a brazen caldron, 
without wetting their clothes, or extinguishing lights which they 
carried in their hands.* Since the middle of the seventeenth cen 
tury, diving-bells have been often used for the purpose of recover 
ing valuable property which had been shipwrecked. 

145. In recent times, the expense attending the construction of 
a diving-bell, and the difficulty of managing so unwieldy a ma- 
How are the compressibility and the impenetrability of air demon- 
strated ? 

How is the power of compressed air to support combustion proved ? 
What is the description of the diving-bell ? 

How are the operators in a diving-bell supplied with air during their 
continuance beneath the surface ? 

What historical account is given of the invention of the diving-bell ? 

* V. Schotti Technics Curiosa, lib. vi. cap. 9. 



DIVING HABITS. 229 

chine j have led to the invention of less operose and more conve- 
nient methods of making submarine investigations; but there is 
one instance of the successful employment of diving-bells for the 
recovery of treasure fro,m the t*ea, which occurred in 1831, and 
that attracted attention on account of the skill and enterprise 
displayed in the conduct of the undertaking. In December, 
1S30, a British frigate having sailed from Rio Janeiro for Eng- 
land, with 810,000 dollars on board, struck on rocks, and was 
sunk at Cape Frio. Captain Thomas Dickenson, an officer on 
that station, obtained permission to attempt the recovery of the 
treasure; and not being able to procure a diving-bell at Rio, he 
adapted to the purpose the ship's iron water-tanks, and constructed 
a huge crane 158 feet in length, and 50 feet above the level of the 
sea, from which to suspend the bells. Though the bells were re- 
peatedly lost, the undertaking was prosecuted by Captain Dick 
enson and other officers, till ultimately 750,000 dollars were re- 
covered, besides a quantity of marine stores and other articles, 

14G. Diving habits, or jackets, adapted for descending under 
water, have been variously contrived ; and among such machines 
are the Scaphandre, invented by the Abbe de la Chapelle;* and 
Klingert's machine for walking under water ; j- but these, though 
ingenious, are probably inferior to the apparatus recently employ- 
ed at Portsmouth, England, by Mr. Deane. The essential part 
of his machinery consists of a capacious metal helmet, covering 
the head and neck, resting on the shoulders, and attached to the 
body by straps. In the front are three oval windows of strong 
plate-glass ; from the lower part of the helmet passes a bent tube 
for the discharge of air which has been breathed ; and from the 
upper part proceeds another tube connected with a flexible pipe, 
through which fresh air is forced from above. Armed with this 
head-piece, and a waterproof dress, the adventurer descends from 
the side of a ship by a ladder to the bottom of the sea, which he 
can explore at his leisure, and walk to any distance within the 
length of his air-pipe. To counterbalance the upward pressure of 
the water at any considerable depth, it is requisite that leaden 
weights should be attached to the body, in addition to the weight 
of the helmet, and thick leaden soles for the shoes.^: 

147. Some curious inventions, for the purpose of submarine na- 

What objection exists to the general use of diving-bells for submarine 
explorations? 

What instance can you cite of the successful employment of these ma- 
chines for the recovery of lost treasure ? 

How is Deane's diving apparatus constructed ? 

What limits the extent to which the diver can extend his examinations 
when using this apparatus ? 

Mow is the body prevented from rising from deep water in the excur- 
sions taken witb diving dresses ? 

* V. Signud de la Fond Elem. de Phys., vol. ii. p. 249- 
f See Tilloch's Philosophical Magazine, vol. iii. p. 172. 
£ Nautical Magazine. 

u 



230 AEROSTATICS. 

vigation, have been invented in the United States. Robert Ful- 
ton, the successful inventor of the steamboat, contrived a machine 
of this kind, called a Torpedo ;* and David Bushnell invented a 
submarine vessel in which a man might pass a considerable dis- 
tance underwater; and by means of this, and its accompanying 
magazine of artillery, an attempt was made to blow up a Bri- 
tish vessel in the harbour of New York, during the late war with 
England, j" This project appears to have failed merely from the 
difficulty or rather impossibility of attaching the magazine to the 
bottom of the ship, which was attempted by means of a sharp iron 
screw, which passed out from the top of the diving-machine, and 
communicated with the inside by a water-joint, being provided 
with a crank at its lower end, by which the engineer was to drive 
it into the ship's bottom. The machine affording no fixed point 
to act from, the power applied to the screw could make no impres- 
sion on the ship; and thus this bold adventure was disconcerted.^: 

Describe the method of Bushnell for blowing up an enemy's ships. 
j Why did this plan prove unsuccessful ? 



* V. Montucla Hist, des Mathemat., t. iii. p. 78. 

t For a description of this curious engine, see a paper on "Submarine 
Navigation," by Charles Griswold, in Silli man's American Journal of 
Science, vol. ii. p. 94. 

^ For a report on Norcross's diving apparatus, see Journal of the 
Franklin Institute for January, 1835, vol. xv. p. 25. 



The following scientific treatises may be advantageously con- 
sulted in reference to the department of Pneumatics : — 

Playfair's Outlines of Natural Philosophy, vol. i. pp. 242 — 262. 

Library of Useful Knowledge, treatise on Pneumatics. 

Gregory's Mathematics for Practical Men, pp. 346 — 352. 

Ferguson's Lectures on Select Subjects, pp. 195 — 227. 

Cambridge Mechanics, p. 377, where the motion of gases is 
treated to some extent, and p. 403, theory of the air pump and 
other machines depending on the atmosphere. 

De Luc Recherches sur les Modifications de 1' Atmosphere. 

Philosophical Transactions, vol. lxvii. pp. 513. 653. 

Cavallo's Philosophy, vol. ii. 

Playfair on the Causes which affect Barometric Measurements, 
in the Edinburgh Philosophical Transactions, vol. i. p. 87. 



ACOUSTICS. 

1. The science which has been designated by the terms Acou- 
stics* and Phonics,! treats of the causes and effects of Sound, and 
the manner in which it is perceived by the organ of hearing - . The 
idea of sound is excited in the mind when the motions which take 
place in any of the bodies around us are such as can be communi- 
cated to the auditory nerve and thence to the brain. This effect 
is produced by means of the organization of the ear, the tremulous 
motions or vibrations of the air being propagated to the tympanum 
or dium, a thin membrane which closes the aperture of the ear; 
behind the drum is a cavity in the bone which forms the side of 
the head, separated by another membrane from an inner cavity, 
from which branch oft variously-formed tubes or canals, which, 
as well as the inner cavity called the labyrinth, are filled with a 
limpid fluid ; and an expansion to the auditory nerve, or delicate 
layer of nervous fibres being distributed over the internal surface 
of the labyrinth and canals, it thus becomes the medium of sensa- 
tion with regard to sound. 

2. There is a passage called the Eustachian tube, which ex- 
tends from the back part of the mouth to the cavity immediately 
behind the membranous drum, through which air passes, and 
therefore the drum vibrates freely when acted on by the sonorous 
undulations of the external air, which are communicated from the 
membrane of the drum by a chain of very minute bones and mus- 
cles passing from it to the membrane over the entrance to the la- 
b) r rinth, and corresponding undulations being produced in the con- 
tained fluid, impressions are propagated to the nervous lining of 
the labyrinth, and thence to the brain. 

3. Hence it must be apparent, that the sense of hearing, de- 
pending as it does on the perfect operation of so complicated an 
organ as the ear, may be impaired by various causes, or entirely 
destroyed when the essential parts of the organ are originally 
wanting, or so greatly injured by disease as to be incapable of 
performing their functions. Thus some persons are born deaf, 
the organization of their ears being so defective that they are ut- 

What is the object of the science of acoustics ? 

Under what circumstances is the idea of sound excited in the mind ? 

How is the effect produced ? 

What is the tympanum of the ear ? 

What is the inner cavity of the ear designated ? 

How is its internal surface lined ? 

What appears to be the immediate instrument of sensation in regard to 
sound p 

What is the position of the Eustachian tube ? 

What is the natural consequence, in regard to language, of an original 
want or an early destruction of the organs of hearing ? 



* From the Greek A*eu.>, to hear, 
t From *«,;, a voice, or sound. 

231 



232 ACOUSTICS. 

terly incapable of perceiving sounds, and therefore can never ac- 
quire the faculty of speech by imitating vocal language. Such 
unfortunate individuals, incapable of obtaining knowledge by the 
usual channels, may, however, be qualified for high degrees of 
mental cultivation by the modes of instruction contrived, or rather 
greatly improved, byL'Epee, Sicard, Braidwood, and others, who 
have most meritoriously devoted their talents to the instruction of 
the deaf and dumb. 

4. Though the functions of the organ of hearing are clearly as- 
certained, as to the general principle of action, yet the peculiar 
purposes of the several parts are by no means equally obvious ; 
nor is it certain that any of them, except the auditory nerve, are 
absolutely essential to the perception of sound. Some persons na- 
turally have an aperture in the membranous drum of the <Jar, and 
in others a similar defect is produced by disease ; but in either 
case, though the faculty of hearing is commonly somewhat im- 
paired, it is not destroyed, not even when, owing to abscess in 
the ear, the chain of bones* between the membrane of the drum 
and that covering the entrance to the labyrinth has been disu- 
nited. In that case, probably, the vibrations of the air impinging 
on the inner membrane cause the requisite undulations in the fluid 
within the labyrinth. 

5. There are persons who occasionally amuse themselves and 
their companions by drawing a quantity of tobacco-smoke into the 
mouth, and then expelling it through one or both ears; a feat 
which can be performed only by those who have a natural or arti- 

^ficial perforation of the membranous drum of the ear; and thus 
they can force the smoke through the Eustachian tube, into the 
cavity of the drum, and discharge it through the perforation just 
mentioned. 

6. In practising the art of diving, it appears that those engaged 
in it on first going into deep water become subject to most intense 
pains in the ears, which continue till they have reached certain 
depths, when the sensation of something bursting within the ear 
with a loud report terminates the pain, and they can then descend 
as low as may be necessary without any further inconvenience. 
There can be no doubt that all this is occasioned by the vast pres- 
sure of the water on the drum of the ear, and its consequent rup- 
ture ; and probably it would be found on investigation, that pearl- 
divers, and others accustomed to deep diving, have the auditory 
faculty more or less impaired. 

What effect on the faculty of hearing has a rupture of the tympanum ? 

What experiment proves the existence of a passage between the mouth 
and the external ear ? 

What sensation precedes the relief obtained by divers when they firs- 
go into deep water ? 

* This chain consists of three distinct bones, called, from their res 
pective forms, the hammer, the anvil, and the stirrup bones, — malleus 
•ncus, and stapes. 



SONOROUS VIBRATION. 233 

7. Though air is the usual medium of sound, it is not essential 
to the formation or the propagation of sonorous vibrations. Some 
substance however, either solid, liquid, or aerial, must form a 
continuous connexion between the sounding body and the ear ; for 
sound cannot be conveyed through a vacuum. If a small bell be 
suspended under the receiver of an air-pump, in such a manner y 
that it can be struck with a hammer without admitting air to it, 
when partial exhaustion has taken place, the sound will be weak- 
ened, and after the rarefaction has been carried as far as possible, 
no sound will be heard on striking the bell. If the experiment 
be made by inclosing the bell in a small receiver full of air, and 
placing that under another receiver from which the air can be 
withdrawn, though the bell when struck must then produce sound 
as usual, yet it will be quite inaudible, if the outer receiver be 
well exhausted, #nd care be taken to prevent the sonorous vibra- 
tions from being propagated through any solid part of the appara- 
tus. 

8. As sounds become weak when the air surrounding the sono- 
rous body is rarefied, so on the contrary, any sound, as that of a 
bell, will be perceived to be much louder when the bell is struck 
in a vessel filled with highly compressed air, than when struck 
with the same force in a vessel of air of the common density. 
Hence, too, it happens that when a pistol is fired on the top of a 
high mountain, where the air is comparatively rare, the report is 
net so loud as when it is fired at the base. 

9. That liquids conduct sound with no less facility than air 
may be ascertained by ringing a bell under water, when it will v 
be heard as distinctly as when rung above the water. And a 
person diving under water would plainly hear the sound of a bell 
struck in the air at a moderate distance. If both the hearer and 
the sounding body be immersed in the same mass of water, the 
sound will appear much louder than when passing through an 
equal extent of air. 

10. The propagation of sonorous vibrations through liquids may 
be rendered visible ; for, on rubbing gently with a wet finger the 
edge of a drinking-glass, half filled with water, sound will be pro- 
duced, and the surface of the water will be covered with minute 
undulations. The intensity or loudness of sound in fluids appears 

What function does the air perform in regard to the sonorous body and 
to the ear ? 

What experiment proves the necessity of a medium for the transmis- 
sion of sound ? 

What is the effect of highly condensed air on the loudness of sounds 
produced within it ? 

What other evidence is afforded of the effect of pressure on the inten- 
sity of sound ? 

How can we prove that liquids conduct sound } 

Does it appear from experiment that liquids are better or worse con- 
ductors of sound than air i 1 

How is the propagation of sonorous vibrations in liquids rendered vi- 
sible ? 

it 2 



234 ACOUSTICS. 

to be augmented in proportion to the increase of their specific gra- 
vity. Thus water, being so much denser a fluid than air, sounds 
produce a stronger effect in the former medium than in the latter ; 
and therefore it may be regarded as a wise provision of the Au- 
thor of Nature, that the organs of hearing in fish are much less 
perfectly developed, and consequently less sensible to the impres- 
sions of sound than those of terrestrial animals. 

11. Solids, when they possess elasticity, convey sounds to the 
ear more readily and effectively than gases or liquids. If a per- 
son, hard of hearing, places one end of an iron rod between his 
teeth, while the other end rests on the edge of an open kettle, he 
will understand what is said by another directing his voice into 
the kettle, more distinctly than if the voice of the speaker passed 
through the air, so that he might converse in this manner with 
any one at a distance at which he would not he^r under common 
circumstances. When a stick is held between the teeth at one 
extremity, and the other is placed in contact with a table, the 
scratch of a pin on the table may be heard though both ears be 
stopped. When sounds are propagated in this manner, the sono- 
rous vibrations must be conveyed through the mouth and along 
the Eustachian tube to the interior part of the organ of hearing. 

12. Among the evidences of the transmission of sound through 
solid bodies, may be mentioned the common experiment of tying 
a ribbon or a strip of linen, cotton, or flannel, to the upper part of 
a large poker, so that it may be supported vertically by holding 
the two ends of the ribbon ; which are to be brought in contact 
with the ears, and pressed against them, so as to close them, then 

« on swinging the poker so that it may strike as gently as possible 
against a bar of the fire-grate, or any other metallic substance, a 
deep sound will be distinctly heard like the tolling of a large bell ; 
and yet if the ribbon be removed from the ears, and the poker sus- 
pended by it, and struck in the same manner, the sound will be 
hardly perceptible. Some experiments will subsequently be no- 
ticed, which show that sound not only passes much more readily 
through elastic solids than through air, but also that it traverses 
the former with abundantly greater velocity. 

13. That peculiar kind of motion in bodies which gives rise to 
the sensation of sound has been characterized by the term vibra- 
tion, because a striking analogy may be traced between the tremu- 
lous agitation which takes place among the particles of a sound- 
ing body, and the oscillations of a pendulum. The nature of so- 
norous vibrations may be illustrated by attending to the visible 

According to what circumstance does their conducting power appear 
to be augmented ? 

What conducting power for sound is possessed by elastic solids com- 
pared with that of other classes of bodies ? 

In what manner may a person partially deaf be enabled to carry on a 
conversation ? 

What easy experiment illustrates the transmission of sounds by solids ' 

What name is given to the motion by which sound is produced * 



NATURE OF SONOROUS VIBRATIONS. 235 

.A motions which occur on striking 01 

,...•;;;..'.! £ — •«•■'".!>•... twitching a tightly-extended cord or 

,■';-- £> .'.."."', '".": ,: " •"••"?;■>.. wire. Suppose such a cord repre- 

t £^:~ o' — ~ ~-^ sen t eo ' °y the central line in the mar- 

'■ : ; . '.lx ' '1 .-•,>' gmal figure to be forcibly drawn out 
'"*• -C";;;- —f t - ;".'.'-••"" to A, and let go, it would immedi- 

ately recover its original position by 
virtue of its elasticity, but when it reached the central point it 
would have acquired so much momentum as would cause it to 
pass onward to c, thence it would vibrate back in the same man- 
ner to B, and back again to b, the extent of its vibration being 
gradually diminished by the resistance of the air, so that it would 
at length return to the state of rest. The string of a violin or a 
harp drawn aside thus, and suffered to vibrate freely, would pro- 
pagate its vibrations to the body of either instrument and to the 
surrounding air, and thus a tone or musical note would be pro- 
duced and rendered perceptible to the ear. 

14. The air usually encompassing sounding bodies on every 
side conveys the sensation of sound in all directions ; therefore 
the aerial vibrations, or, as they have been termed pulses, must be 
communicated successively and generally throughout the whole 
space within the limits of which they are capable of affecting the 
ear. We may conceive this to happen in consequence of minute 
expansions and contractions of the particles of air, which, thus 
pressing on the contiguous particles around them, excite corre- 
sponding motions, extending every way from a common centre. 

15. These soniferous undulations of the air have been compared 
to the waves spreading in concentric circles over a smooth pond 
of water when a stone is thrown into it. And thus as the liquid 
waves are propagated not only directly forward from the centre, 
but also if they encounter any obstruction, as from a floating bor 
dy, they will bend their course round the sides of the obstacle and 
spread out obliquely beyond it, — so the undulations of air, if in- 
terrupted in their progress by a high wall, or any similar impedi- 
ment, will be continued over its summit, and propagated on the 
opposite side of it. From this description of the nature of sono- 
rous vibration it will be perceived to consist of the alternate dila- 
tion and compression of certain portions of air or other bodies act- 
ing mechanically, so as to cause corresponding effects throughout 
a given space ; and the motion thus originated, produces no per- 
manent change of place among the particles of the sonorous mass, 
hut simply an agitation or tremor, so that each particle, like a 

What figures are successively assumed by a string or wire thrown into 
a slate of vibration ? 

What purpose is served by the body of a stringed instrument ? 

How are aerial vibrations or pulses communicated ? 

llow may this communication be accounted for without supposing the 
particles of air to move out of their respective places ? 

To what have soniferous undulations been compared i 

What analogous effects favour the supposition of their similarity ? 



236 ACOUSTICS. 

pendulum that has been made to oscillate, recovers at length its 
original position. Hence sound is communicated through the at- 
mosphere by the propagation of minute vibrations of its particles 
from one part of the fluid mass to another without any translation 
in motion of the fluid itself. 

16. " Perhaps we may most distinctly conceive the kind of fact 
here spoken of, by comparing- it to the motion produced by the 
wind in a field of standing corn : grassy waves travel visibly over 
the held in the direction in which the wind blows, but this appear- 
ance of an object moving is delusive. The only real motion is 
that of the ears of grain, of which each goes and returns as the 
stalk stoops and recovers itself. This motion affects successively 
a line of ears in the direction of the wind, and affects simultane- 
ously all the ears of which the elevation or depression forms one 
visible wave. The elevations and depressions are propagated in 
a constant direction, while the parts with which the space is fill- 
ed only vibrate to and fro. Of exactly such a nature is the pro- 
pagation of sound through the air. The particles of air go and 
return through very minute spaces, and this vibratory motion runs 
through the atmosphere from the sounding body to the ear. Waves, 
not of elevation and depression, but of condensation and rarefac- 
tion, are transmitted ; and the sound thus becomes an object of 
sense to the organ."* 

17. That vibration of the particles of bodies which has been 
indicated as the cause of sound must have a certain degree of ve- 
locity in order to produce the required effect. An extended coTd 
may be so slack that when made to vibrate it will yield no sound, 
its motion being too slow and weak to propagate sonorous undu- 
lations through the surrounding air. In order that sound may be 
procured the tension of the cord must be increased ; and it will 
then be found, that the length remaining unaltered, the number of 
vibrations in a given time will be augmented in proportion to the 
additional tension of the cord. 

18. It has been ascertained by experiment that a vibrating cord 
will not produce a sound distinctly appreciable by the most deli- 
cate ear, when it makes less than about 32 vibrations in a second. f 
But the susceptibility of the organs of hearing to grave or acute 
sounds appears to be different in different individuals. There are 
some curious observations on this subject in a paper published in 

To what natural appearance may we compare the soniferous waves ? 
Of what real nature are the waves of air ? 

"Will every degree of tension in a cord enable it to produce audible 
sounds ? 

What has experiment proved in regard to this matter ? 

Are all ears equally susceptible to the same classes of sound ? 

* Whewell's Astronomy and General Physics considered with Refe- 
rence to Natural Theology, b. i. ch. xiv. pp. 117, 118. 

t Savart asserts that he has proved by experiment, that a perceptible 
sound is produced by a cord giving eight single vibrations in a second. — 
En. 



LIMITS OF AUDIBLE PERCEPTION. 237 

the Philosophical Transactions, by Dr. Wollaston, " On Sounds 
Inaudible by certain Ears." The attention of this ingenious 
philosopher was attracted by the circumstance of finding- a person 
insensible to the sound of a small organ-pipe, which, with respect 
to acuteness, was far within the limits of his own hearing - . He 
was hence led to try the effect of different modes of weakening 
the sense of hearing in himself; and he found that by closing the 
nose and mouth, and expanding the chest, the membrane of the 
drum of the ear, being subjected to extraordinary tension by ex- 
ternal pressure, made the ear insensible to grave tones, without 
affecting the perception of sharper sounds. 

19. This fact affords some evidence in favour of the opinion 
that the membranous drum of the ear, by means of its apparatus 
of bones and muscles connecting it with the internal membrane 
over the labyrinth, is capable of tension and relaxation so as to 
adapt itself to receive and transmit aerial undulations having dif- 
ferent degrees of velocity ; and hence it may be concluded that 
the power of perception of low or high tones depends on the state 
of the membrane of the drum and parts united to it. 

20. The range of human hearing includes more than nine oc- 
taves, the whole of which are distinct to most ears, though the 
vibrations of a note at the higher extreme are six or seven hundred 
times more frequent than those which constitute the gravest audi- 
ble sound; and as vibrations incomparably more fiequent may 
exist, we may imagine, that animals like the Grylli (crickets or 
grasshoppers), whose powers appear to commence nearly where 
ours terminate, may hear still sharper sounds, which we do not 
know to exist ; and that there may be insects hearing nothing in 
common with us, but endued with a power of exciting, and a sense 
that perceives the same vibrations which constitute our ordinary 
sounds, but so remote that the animal who perceives them may be 
said to possess another sense, agreeing with our own solely in the 
medium by which it is excited, and possibly wholly unaffected 
by those slower vibrations of which we are sensible."* 

21. Though sound may be propagated through an infinite mass 
of air to very considerable distances, yet its intensity or loudness 
diminishes in proportion as the sonorous vibrations extend from 
the spot where they are produced. The rate of diminution of in- 

What facts did Dr. Wollaston observe on this subject ? 

In what manner may the sense of hearing for grave tones be volunta- 
rily weakened ? 

On what is the power of perceiving sounds of different degrees of 
acuteness probably dependent ? 

How extensive is the range of human hearing ? 

What difference in the degree of frequency must exist between the 
extremes of the audible scale ? 

What are probably the endowments of insects in regard to sound ? 

How is the intensity or loudness of sounds affected by the distance 
from the sonorous body ? 

* Abstracts of Pap. in Philos. Trans., vol. ii. p. 133. 



Zd# ACOUSTICS. 

tensity may be inferred from mathematical calculation as well as 
ascertained by experiment; and the results, which confirm each 
other, show that other circumstances being- alike, the intensity of 
sound will be the inverse ratio of the square of the distance of 
the place of observation from the sounding body. The distance 
to which sound can be transmitted through the atmosphere, de- 
pends in some degree on the direction of the wind and local cir- 
cumstances. Most persons residing within a few miles of a very 
large bell must have observed that the sound of it will be audible 
or otherwise, in certain situations, according to the quarter from 
which the wind blows. Under favourable circumstances sounds 
may be conveyed to great distances. Instances are recorded of 
the report of a cannon having been heard thirty leagues from the 
place where it was fired.* 

22. The absolute velocity with which sound is propagated 
must depend on the nature of the medium by which it is conve) T ed. 
Atmospheric air being the general medium of sound, the investi- 
gation of its conducting power has at different periods occupied 
the attention of men of science. Cassini, Picard, and Roemer, 
members of the French Academy of Sciences, in the latter part 
of the seventeenth century, made experiments from which they 
inferred that sound travels 1172 feet in a second of time ; Dr. Halley, 
and Flamstead, the astronomer royal, who pursued the inquiry in 
England, were led to the conclusion that the common velocity of 
sound was 1142 feet in a second ; and this deduction was confirm- 
ed by the varied and extensive researches of Dr. Derham, in con- 
sequence of which it has been generally adopted by subsequent 
writers on this branch of science. This statement, however, is 
now considered as requiring some correction on account of the 
influence of temperature ; and from a comparison of the experi- 
ments of Derham made in the day-time, with some more recent 
nocturnal observations of French academicians, it appears that the 
actual velocity of sound, at the zero of temperature of the centi- 
grade thermometer (32 deg. of Fahrenheit) is about 1130 feet in 
a second ; which likewise agrees with other accurate experiments 
of professor Pictet of Geneva. 

23. By adopting either of the numbers last stated sufficiently 
correct calculations may be made of the distances of objects as 
inferred from the relative velocities of light and sound ; the for- 

According to what law does it vary ? 
On what does the absolute velocity of sound depend ? 
What is the absolute velocity of sound in air at 32° Fahrenheit ? 
How is a knowledge of that velocity applicable to the measure of dis- 
tances ? 



* When the explosion of the volcano of Cotopaxi, in Peru, took place, 
in January 1803, the noise it occasioned was heard day and night, like 
continued discharges of artillery, at the port of Guayaquil, 52 leagues 
distant, by the travellers Humboldt and Bonpland — Edinburgh Review 
for Xuv. 1814, vol.xxiv. p. 142 ; from Humboldt's Researches. 



VELOCITY OF SOUND. 2341 

mer from its extreme celerity being regarded as appearing instan- 
taneously* on its production, at distances not exceeding 1 a few 
miles. Thus supposing' a flash of lightning to be perceived, and 
on counting the se onds that elapse before the thunder is heard, 
we find them to amount to 3i ; then if we reckon the velocity of 
sound at the rlite of 1130 feet in a second, it will follow that the 
thunder-cloud must be distant 1130 X 3!== 3955 feet. In the same 
manner may be discovered the distance of a ship at sea, if we 
see the flash of a gun fired from it, and ascertain the number of 
seconds that elapse before the report becomes audible. In defect 
of a stop-watch a rough estimate of time may be made by any 
person, by counting the pulsations of the artery at his wrist, which 
in most young people in health will amount to about 70 in a 
minute. 

21. Sounds are propagated with greater or less velocity through 
gases according to their density; and thus a sharper tone will be 
produced by a sonorous body in hydrogen gas than in atmos- 
pheric air, and a graver tone by the same body in carbonic acid or 
fixed air. Vapours of water, spirit of wine, or ether, are capable 
of conveying sounds with degrees of facility proportioned to their 
respective densities, as appears from experiments made at Arcueil, 
near Paris, by Biot, Berthollet, and Laplace, the first-mentioned 
of whom published an account of their investigations in 1807. 
The vapour of ether conveys sound almost as readily as atmos- 
pheric air; for a bell, the sound of which in air could be heard 
at the distance of 158.5 yards, was heard in the vapour of ether 
at that of 143.7 yards. f 

25. Experiments on the conduction of sound by water were 
made a few }^ears ago, by Messrs. Colladon and Sturm, in the lake 
of Geneva. The method of operation was to sink a large bell seve- 
ral feet below the surface of the water, strike it a smart blow with 
a hammer, the handle of which at the same instant brought a blaz- 
ing port-fire in contact with half a pound of gunpowder to produce 
a signal. The sound was heard nine miles by means of a spe- 
cies of ear trumpet, sunk in the water, and having a broad spade- 
like surface facing the direction in which the sound came. The 
times were accurately noted, and the distances having been care- 
fully determined by triangulation, the velocity, per second, was 
found to be 4709 feet.;}: 

To what expedient may one resort when not furnished with a time- 
keeper to note the time elapsed between the perception of light and of 
sound in any given explosion ? 

How are the different gases related to each other in regard to the 
transmission of sound? 

With what proportionate velocities do the vapours of different liquids 
conduct sound ? 

In what manner has the conducting power of water been determined ? 

* See Treatise on Optics. 

+ See Nicholson's Philosoph. Journal, 1812, 8vo. vol.xxx. pp. 109. 173. 

j: See Aunales de Chym. et de Phys. vol. xxxvi 



240 A«JOXJSTICS. 

'2fi. Examples have been already adduced of the facility witn 
which solid bodies transmit sounds. To these it may be added. 
that the North American Indians avail themselves of this pro- 
perty of solid matter, applying their ears close to the ground in 
order to discover the noise made by approaching enemies, when 
the distance is too great for the sounds to be conveyed through 
the air. Upon the same principle is founded the utility of the 
stethoscope,* an instrument invented some years since by Dr. 
Laennec, a French physician, to ascertain the state of the cavities 
o{ the body, especially the chest, as to health or disease. It con- 
sists of a wooden cylinder, one end of which being placed in con- 
tact with the surface of the body to be examined, and the other 
resting- against the ear of the observer, then by gently striking 
the body with the knuckles or otherwise, sounds will be perceived 
indicative of the existence of abscess, schirrus, or any other altera- 
tion of structure which may have taken place. 

27. Dr. Chladni, a German philosopher, who distinguished 
himself by his investigations relative to acoustics, estimated the 
velocity of transmission of sounds by the tone produced by vibra- 
tion, or in other words, by the musical note emitted by a rod or 
bar of /any substance when struck. By thus comparing the sound 
of a rod made to vibrate longitudinally with that of a column of 
air vibrating in a tube of the same length, he found that the velo- 
city of sound in air being represented by 1, the velocity of 
sound transmitted by tin would be - - - - 7| 

By silver 9~ 

By copper --------- 12 

By iron -------- -17 

By different kinds of wood - from 11 to 17 

Iron and glass appear to be among the best conductors of sound, 
which they transmit at the rate of 17,500 feet, or more than 3 miles 
in a second. 

28. Some very interesting experiments on the capacity of solids 
to conduct sounds were made by M. Biot, at Paris, in which the 
research was prosecuted by more direct means than those last 
stated, and different results were obtained, whence the velocity 
of the transmission of sound through cast iron appears to be in- 
ferior to the prece-ding estimate. M. Biot took advantage of the 
circumstance of laying down trains of cast-iron pipes in the French 
metropolis to form an aqueduct 3120 feet in length. At one ex- 

Wbat peculiar use do the American Indians make of the conducting 
power of solids ? 

What purpose does it serve in the practice of medicine ? 

What is the construction and use of the stethoscope ? 

What is the relation of the metals to each other in regard to the con- 
duction of sound ? 

What solids appear to he among the hest conductors of sound ? 

In what manner did Biot determine the relative conducting power of 
iron and of air ? 

* From the Greek Hr'^h,, the breast, or chest, and ixj.-rs^, to examine 



TRANSMISSION OF SOUND THROUGH SOLIDS. 241 

trcmity of the tubes was fitted a ring of metal cf the same diameter 
as the orifice, in the centre of which were fixed a clock-bell and a 
hammer which could be made to strike at pleasure, in such a man- 
ner that the hammer would fall on the bell and on the ring - of metal 
just mentioned at the same instant : thus the sound of the latter 
being: transmitted through the solid metal or tube itself, and that 
of the former through the aerial canal or cavity of the tube, the 
perceptible difference of the time of transmission by the respec- 
tive mediums might be determined. It was found that by placing 
the ear against the other extremity of the pipe two sounds were 
distinctly -heard, and the time being very accurately noted, by 
means of a seconds watch, it appeared from a mean of many ex- 
periments that sound is transmitted with 10^ times greater velocity 
through c-ast iron than through air, travelling through the former 
at the rate of 11,865 feet in a second. 

29. It is a commonly-received opinion that acute and grave 
sounds are transmitted in all directions with equal velocity; and 
an experiment made by M. Biot on the same train* of pipes that 
served for those just recorded tends to confirm it. He caused a 
man at one extremity of the train to play various airs on the flute, 
placing himself at the other end to observe the effect. Now a 
piece of music consisting of a series of notes varying from acute 
to grave and the contrary, and forming a peculiar ^melody, adapted 
to a certain measure, which regulates strictly the intervals of the 
successive tones, it must follow that if at the' distance of 3120 
feet any difference had been perceived in the velocity of the dif- 
ferent notes, the music would have become confused and imperfect 
at the distance just stated. This, however, was by no means the 
case, the melody being as perfect when thus listened to as in the 
immediate focus of the sounds. 

30. There can be no doubt that acute and grave sounds are trans- 
mitted through spaces of no very considerable extent without any 
perceptible difference of velocity ; for otherwise there could be no 
such thing as harmony, or the concord of sounds varying in tone 
or pitch, except in the immediate vicinity of the source of sound. 
But that all sounds pass with equal celerity through the same me- 
dium to any imaginable distance seems improbable ; and more 
numerous and precise experiments than have hitherto been made 
would be requisite in order to enable us to decide the point in 
question. 

31. Sounds certainly in some respects interfere with each other. 
Thus one sonorous body being made to vibrate, all others near it 

What was the result of his experiments ? 

What is the rate of transmission of grave compared with that of acute 
rounds ? 

How did Biot conduct his experiments on this subject ? 

Why are we allowed to suppose an equally rapid transmission for sounds 
of all degrees of acuteness ? 

What occurs when of several sonorous bodies near each other, and 
tuned to accord, one is thrown into a state of vibration ? 

X 



212 ACOUSTICS. 

capable of producing the same tone will vibrate also ; and there- 
fore when one body is made to produce a certain note, probabl}' 
its soniferous vibrations would be checked or interrupted by the 
emission of a more powerful or discordant sound from another 
body near it. Hence weak sounds generally are drowned by loud 
ones ; and on the contrary, during the silence of night, many gen- 
tle sounds become perceptible which, amidst the din arising from 
daily labour, business, and pleasure, especially in a crowded city, 
are completely stifled ere they can reach the ear. 

Theory of Musical Sounds. 

32. Most persons, in whom the sense of hearing is perfect, pos- 
sess the faculty of distinguishing certain relations between sounds 
differing in tone, that is, being more or less grave or acute one 
than another ; and such persons are said to have a musical ear, or 
an ear for music,* because pieces of music consist of combinations 
of such tones or sounds as those just mentioned. The manner in 
which musical sounds are formed by different instruments, and 
the peculiar circumstances on which their mutual relations depend, 
will now be the subject of investigation. 

How are weak sounds affected by the occurrence of more powerful 
ones in their vicinity ? 

What is meant by " a musical ear?" 

* There are persons who, though endowed with the sense of hearing 
in perfection, yet appear to be utterly destitute of an ear for music. 
They seem to have no perception whatever of the pleasure generally ex- 
cited by successions of melodious sounds, and therefore (if their own 
professions are to be believed) they cannot properly distinguish one tone 
from another, or discriminate between the noise of an itinerant music- 
grinder and the performance of a musician possessing exquisite skill and 
taste. It would be unreasonable and unjust to attribute the alleged indif- 
ference of such persons to caprice, and to doubt their veracity ; for it 
would be difficult to point out any motive which could induce a person to 
counterfeit an insensibility to the " concord of sweet sounds." The 
writer of this note heard a clergyman of his acquaintance, after having 
witnessed the singing of Catalani, declare that he was utterly unable to 
ascertain in what respect her performance excelled that of a common 
ballad-singer, gravely averring that he thought the melody of the one 
just as agreeable as that of the other. It is deserving of notice that indi- 
viduals distinguished for poetical talent have been destitute of an ear for 
music. This was the case with the celebrated poet Pope, one of the 
most exquisitely skilful masters of the melody of verse that ever existed, 
who was unable to perceive any difference between the compositions of 
Handel and the vilest attempts of a wandering fiddler. It appears, like- 
wise, that a highly distinguished poet of the present age, Sir Walter 
Scott, though not incapable of enjoying music when performed by others, 
was utterly unable to acquire a practical knowledge of music ; and that 
when young, having been placed under the tuition of an eminent teacher 
of music at Edinburgh, the attempt to instruct him was relinquished, 
after a short time, on the ground that he was totally deficient in that in- 
dispensable requisite for acquiring the art — a musical ear. — See Annual 

iography, vol. xvii. p. 179. 



MUSICAL SOUNDS. 243 

33. It .Has been already stated that the character of a sound as 
to gravity or acuteness, is determined by the number of vibrations 
in a given time made by the sounding body, and thence propagated 
through the air, or some other medium, to the ear. A sonorous 
body,"as for instance, a bell, the dimensions and general form of 
which remain unaltered, will, when struck, always emit the same 
sound ; for though its sonorous vibrations may be more or less 
powerful according to the manner in which it is struck, they will 
always be isochronous, or equal in equal times. Suppose then a 
series of three bells to differ relative^ in size, so that the largest 
should vibrate when struck 256 times in a second, the next 512 
times, and the smallest 1024 times, it would be found that the first 
bell would yield the sound or tone called middle C of the piano- 
forte or harpsichord, or that note produced by pressing down the 
central key of the instrument ; the second bell would yield a tone 
an octave above the former ; and the third bell one an octave 
higher still ; for the larger bell would yield the graver sound. 

34. The number of vibrations which take place in a sounding 
body, and the consequent tone which it yields, depend on several 
circumstances connected with the peculiar form and consistence 
of the body ; and hence the variety of musical instruments, the 
distinguishing properties of which depend on the diversity of 
modes in which harmonious sounds can be formed and propagated. 
The manner in which the tones are emitted by an extended string 
or wire will afford an example of the modifications of sound pro- 
duced by alterations of the state and condition of the string as to 
its dimensions and tension. 

35. 1. When two strings of equal diameter are equally stretch- 
ed, the relative numbers of their vibrations, and of the consequent 
tones they yield, will be in the inverse ratio of their lengths : thus 
if two strings A and B have the same size and tension, and if A 
have double the length of B, the former will vibrate only half as 
many times in a second as the latter, and w r ill yield a note an oc- 
tave below the latter, 

2. When strings have the same length and tension, the num- 
bers of their vibrations and respective tones will be in the in 
verse ratio of their diameters. 

3. When strings have the same diameter and the same length, 
the numbers of their vibrations and relative tones will be in the 

What remarkable examples may be cited of persons wanting this fa- 
culty ? 

What relation always subsists between the vibrations of a sonorous 
body of invariable dimensions ? 

What numbers of vibration must three bells make in order that their 
tones should be an octave apart, and the lowest one correspond with the 
middle C of the piano ? 

On what circumstances does the number of vibrations in a sounding 
body depend ? 

What relation subsists between the numbers of vibrations compared 
with the le?igths of strings ? 

What, compared with their diameters ? 



244 



ACCrr.Tirr 



direct ratio of the square roots of the weights by which they are 
st retched. 

36. It will easily be conceived that a string" may be extended 
so slackly, that when made to vibrate, no audible sound will be 
produced; and from experimental observations it may be inferred 
that a string vibrating less than eight * times in a second will not 
yield a perceptible sound. 

37. Columns of air included within tubes, when thrown into 
the state of sonorous vibration, yield tones bearing certain relations 
to their lengths; and other circumstances remaining unaltered, a 
tube of any given length capable of yielding a musical tone, will, 
when reduced to half that length, yield a tone an octave higher 
than before. The following scale will show the relative lengths 
of open tubes requisite to produce a succession of octaves, com- 
mencing from the lowest audible sound, and with the numbers of 
the vibrations taking place during the emission of each sound. 

Scale of Octaves corresponding luith certain lengths of open Organ- 
pipes. 



rrH- 


,32 


■16 


8 


4. 


£> 


i 


£ 


■■■ 


k 


Feet 

! 




dsL_ 
















■r- 


-!— 

i 






Mi— 














1= 


£ 




— 


■-...C-A 31 

-&H 


rf- 




















1 


"^£2: == h 

^ 


7# 












- ,.-, 








1 


— c^M^ — 


tty- 






















_^<^ 


■fe£ 










. 


1 










-B&* 


IF1I 








I 

— 


hr 












—^-^ , 








I 


- 












f 








.-■.- 
















-.-tj-El 1 







■ 














1 


_^-ii5L_ 






























- el 
















1 


c X>r< 




■ 1= 


















■ I 


^G^l 


;~ . 


32 


— - 


s.j.-h 


256 


^12, 


ioa_ 


2G4S 


4096 


8192 


1 


-&A^ 



Semi-vibrations in one Second. 

38. Those who have any acquaintance with musical notation 
will, on inspection of the preceding table, perceive that the third 

What, compared with the stretching 1 weights or tensions? 

What is the relation, in point of acuteness, between the tones of a pipe 
of a given length and of one but half that length ? 

Through how many octaves in music may pipes rise by diminishing 
their length from 52 feet to 1^ inches ? 



* As proved by Savart, 
Ann. de Chim. vol. xxxvi. 



-Revue Encyclopedique. Juillet, 1831, and 

-Ed. 




MUSICAL SOUNDS. 245 

and fourth staves marked with the treble and bass clefs, with the 
single line between them, include three octaves, while the lines 
above the treble clef and those below the bass clef may all be 
considered as so may ledger lines. Persons who have no know- 
ledge of music may be informed, that this scale of nine octaves 
not only includes the utmost range of musical tones ever employed 
in practice, but also that the notes at either extremity of the scale 
are rarely introduced, but few instruments being adapted for the 
production of such tones. 

39. The numbers at the bottom of the foregoing scale denote 
the half vibrations performed respectively in a second by the seve- 
ral columns of air whose lengths are stated above. Sonorous 
vibrations, like those of a pendulum, extend on either side of the 
point occupied by the vibrating body when in the state of rest. 

Suppose A B, in the marginal figure, to be an ex- 
tended string or wire ; if it be drawn aside to C, and 
suffered to vibrate, its oscillations will carry it alter- 
nately on either side of the central point E ; and its 
passage from C to E may be termed a semi-vibration, 
but when it has arrived at E, its momentum will cause 
it to proceed to D, and thus a complete vibration must 
include a certain space on either side of the central 
point or line of rest, to which the string will gradually 
return as its motion progressively declines through 
the resistance of the air. 

40. If we consider the manner in which sound is propagated, 
it will be manifest that it can only affect our ears by means of 
semi-vibrations, for the sonorous undulations of air or any other 
conducting medium consist of contractions and dilations through 
indefinitely minute spaces ; and the impression of any particle of 
air on the drum of the ear must be made in its semi-vibration to- 
wards the ear, while the corresponding semi-vibration will act in 
the opposite direction. 

41. Hence, in estimating the relations between the tones of a 
sonorous body, as the string of a harp or pianoforte, and the num- 
ber of its isochronal vibrations, it is usual to reckon the complete 
vibrations ; and therefore the number of effective or perfect vibra- 
tions answering to each of the notes in the preceding scale will 
be just half the number stated at the bottom of the scale ; and 
these numbers will correspond with those of the sonorous vibra- 
tions of bells mentioned above. 

42. Musical instruments yield not only octaves, but also a 

How extensive is the actual range ordinarily employed in musical com- 
position ? 

What resemblance exists between the oscillations of a pendulum and 
the vibrations of sonorous bodies ? 

How is it customary to reckon the number of vibrations of a sonorous 
body ? 

What is the difference between one tone and another on a musical in- 
strument, commonly called ? 

x2 



2iG ACOUSTICS. 

variety of intermediate tones, which have certain relations to each 
other; and the difference between one tone and another, is termed 
an interval. When two tones or notes sounded together produce 
an agreeable effect on the ear, the combination is called a musical 
concord ; and when the effect is disagreeable, it is called a dis- 
cord. It appears from experiment, that any two notes will form 
a consonance or concord, more or less perfect in proportion as the 
relation between the numbers of their vibrations is more or less 
simple. Thus if one note is the result of a number of vibrations 
double that of those belonging- to another note, the former will be' 
an octave to the latter, and their vibrations will be relatively as 
2 to 1. 

43. It has been already shown, that any series of vibrations 
successively duplicates of those preceding them will form so 
many octaves, all denoted in the gamut or musical alphabet by 
the same letter. Indeed the agreement between notes produced by 
aseries of vibrations, when those corresponding with the higher or 
acuter note are exactly double, quadruple, eight times, &c, those 
corresponding with the lower note, is so perfect, that in musical 
composition, octaves are considered as having the same effect with 
notes whose vibrations are equal, and which are therefore said to 
be in unison. 

44. The common musical scale or gamut imcludes seven inter- 
vals, between one octave and that next above or below it, and 
consequently it consists of eight notes taking in the two octaves. 
These notes have been distinguished by certain names, each form- 
ed of a single syllable ; but it is more usual for teachers of music, 
in this country at least, to designate the notes by the first seven 
letters of the alphabet, and thus the octaves are always denomi- 
nated by the same letter as that from which the scale begins. 

45. In any series of notes or tones the number of corresponding 
vibrations will alwa}~s increase in a certain ratio to the increased 
acuteness of tone; and on the other hand, if the notes be pro- 
duced by a string of a given diameter and tension, its length must 
decrease in proportion to the increase of sonorous vibrations and 
acuteness of tones. The relations between the numbers of sono- 
rous vibrations and the lengths of strings required for the produc- 
tion of the notes forming a single octave will appear from the fol- 
lowing table of the notes of the gamut, or diatonic scale : 

What is meant by the terms concord and discord? 

How is the relation of the numbers of vibrations required for two 
notes, connected with their respective effects on the ear ? 

What relation has the number of vibrations in a string producing a 
given tone to that of another sounding an octave below ? 

How are octaves regarded in musical composition ? 

How many intervals has the common musical scale or gamut? 

How are the notes designated ? 

How will the number of vibrations in any series of notes always be 
compared to the acuteness of tone ? 

When a string of given diameter and tension is considered, how will 
the acuteness of notes vary ? 











MUSICAL INTERVALS. 




^47 






Names 


of Notes. 


Relative Number 
of Vibrations. 


Relative Lengths 
of Strings. 


c 


- 




- 


ut 


- 


1 


- 


1 


D 


_ 




- 


re 


- 


9-8 


- 


8-9 


E 


_ 




- 


mi 


- 


5-4 


- 


4-5 


F 


_ 




- 


fa 


.. 


4-3 


- 


3-4 


G 


_ 




_ 


sol 


. 


3-2 - 


- 


2-3 


A 


- 




- 


la 


. 


5-3 


- 


3-5 


B 


- 




- 


si 


- 


15-8 - 


- 


8-15 


C 


- 




- 


ut 


- 


2 


- 


1-2 



46. Such is the musical scale that appears to be founded on the 
relations between sonorous vibrations and the perceptive powers 
of man ; for it has been generally adopted with slight modifica- 
tions by the inhabitants of all countries with whose music we 
have any acquaintance. A comparison of this table with the scale 
of octaves in a preceding page will show how the gamut may be 
applied to successive octaves, the notes in every octave being 
divided by similar intervals from each other. 

47. The eight or rather seven notes of the gamut (the last, 
being an octave of the first,) are not however separated by equal 
intervals. On observing the relations between the different num- 
bers of vibrations, we shall find that the relation or interval be- 
tween C and D is as 8 to 9 ; that between D and E, as 9 to 10 ; 
between E and F, as 15 to 16 ; between F and G, as 8 to 9 ; be- 
tween G and A, as 9 to 10; between A and B, as 8 to 9; and 
that between B and C, as 15 to 16. Thus it appears that the 
intervals £, !■, £, % and £, are nearly equal ; and they are there- 

ibre regarded as whole tones ; but the intervals ^. and £ are but 
little more than half either of the others, and hence they are 
named semi-tones. In transposing pieces of music from one key 
to another, attention must be paid to the places of the semi-tones, 
and hence the principal use of the marks called flats and sharps ; 
the effect of which cannot be understood without some practical 
acquaintance with music. 

48. But though this gamut or musical scale may be considered as 
the groundwork of all existing music, it must be admitted that it 
does not appear to have been always known or adopted in its pre- 
sent state, but to have formerly consisted of those notes only 
which are separated by complete intervals or whole tones ; for, 
in the old Scotch and Irish tunes, the semi-tones are wanting, 
and hence the peculiar effect of the national music of those 
nations. And it has been stated that the oldest national airs 

What is the relative number of vibrations required to produce G of 
the diatonic scale, when the C below it is produced by a number taken as 
unity ? 

What will be the relative lengths of string in the two cases ? 

On what is the generally received musical scale apparently founded ? 

Are all the intervals of the gamut equal ? 

State the actual intervals between the several letters. 

Of what did the gamut formerly consist? 

What notes of the scale are wanting in the music of several nations? 



248 ACOUSTICS. 

of the Orientals, the people of the North of Europe, and even 
those of the Italians, exhibit the same characteristic omission of 
the notes F and B, thus increasing the intervals now occupied by 
the semi-tones in the received scale, so as to make them exceed 
whole tones. 

49. The combination of notes into a successive series, in which 
one musical tone or sound is heard at a time, constitutes melody 
or air in music ; while the synchronous production of sounds, or 
the union of two or more successions of musical tones is requisite 
to form harmony or music in parts. There is thus a radical dis- 
tinction to be made between melody and harmony, sometimes im- 
properly confounded, the former consisting of music simple and 
unaccompanied, and the latter of music in a more complex and 
artificial form. 

50. The construction of harmony or composition of accompani- 
ments for musical airs requires an acquaintance with the concords 
and discords of the scale of notes ; in order that the composer 
may know how to introduce them in such a manner as to gratify 
the ear and produce the highest effect. Next to the octave, the 
most perfect consonance of tones is that produced when the num- 
bers of the vibrations of two notes are in the ratio of 3 to 2, or 
when the lower note is formed by a string or other sonorous body 
which makes but 2 vibrations, while the string forming the high- 
er note makes 3 vibrations. Such a concord is called a fifth, as 
& in the preceding table ; C, the lower note, being formed by a 
string which may be 1 foot in length, and G, the fifth note above 
it, by a similar string only f of a foot in length. 

51. If the ratio of the vibrations be as 5 to 4, that is, if the low- 
er note makes 4 vibrations in the same time that the higher makes 
5, the concord called a third will be produced, as £. When the 
ratio of the vibrations is as 5 to 3, the lower note making 3 vi- 
brations while the higher makes 5, the concord called a sixth will 
be produced, as ( A . And if the ratio of the vibrations be as 4 to 3, 
the lower note making 3 vibrations while the higher makes 4, the 
interval will be a fourth, as £, which is sometimes reckoned a con- 
cord, as the effect in harmony is not unpleasing. The same ob- 
servation will apply to the minor third, in which the ratio is that 
of 5 to 6, as £; and the minor sixth, in which the ratio is as 5 to 8, 
as E , the lower note E making 5 vibrations, while the higher C 
makes 8. 

52. The discords are the second and seventh, the former of 

What constitutes melody ? 

To what art is the knowledge of musical concords and discords requi- 
site ? 

"Which concurrence of notes gives next to the octave the most agreea- 
ble impression i 3 

What are the relative numbers of vibrations produced by strings 
yielding the concord of fifths? 

How is the third produced ? sixth? fourth? 

How are the minor third and the minor sixth respectively produced ? 

Which two sets of notes sounding together produce the discords ? 



VIBRATIONS OR WAVES. 249 

which produced by two notes sounding 1 tog-ether, the interval be- 
tween which is only a tone or a semi-tone, is particularly disa- 
greeable. The major seventh is the discord produced by notes 
whose vibrations are in the ratio of 9 to 16, as £; and the minor 
seventh is also a discord, arising from notes whose vibrations are 
in the ratio of 8 to 15, as ° : both these are sometimes intro- 
duced. 

53. The absolute number of vibrations necessary to constitute 
any given tone or musical note can hardly be determined with per- 
fect accuracy ; for the tone of an instrument which might be pre- 
sumed to be permanent, as a bell or an organ-pipe, can hardly be 
supposed to be unaffected by the state of the air ; besides which, 
there may be other circumstances which may cause occasional 
variation in the number of the sonorous vibrations even of a bell. 
Nor is it probable that the vibrations of a string or wire, under the 
same circumstances of length, diameter, and tension, would yield 
exactly the same number of sonorous vibrations, in different states 
of the atmosphere, and under different degrees of temperature. 

54. Hence considerable difficulties would attend any attempt to 
ascertain by experiment the relations between sounds or tones, and 
the vibrations of the sounding bodies. It appears, however, from 
a paper in the Memoirs of the Royal Academy of Sciences at Ber- 
lin, 1823, that some results have been obtained, as the fruit of 
experimental researches, which agree as nearly as could be ex- 
pected with theoretical estimates previously made, and which 
may therefore serve as the basis of future calculations of the num- 
bers of sonorous vibrations corresponding with the different tones 
and semi-tcnes of the musical scale. 

55. The tone or note whose corresponding vibrations have been 
made the particular object of investigation is that marked A, oc- 
cupying the second space from the bottom in the stave distin- 
guished by the treble clef, being the note produced by the third 
string of the violin, and a sixth above middle C of the pianoforte. 
The following 1 are the numbers of the vibrations or waves in a 
second connected with the note in question, as deduced from ob- 
servations made in different orchestras : 

Theatre at Berlin - 437.32 

Italian Opera at Paris - - 424.17 
French Opera - - - 431.34 
Comic Opera - 427.61 

56. The difference between these numbers serves to corrobo- 
rate the remarks already made on the difficulty of deciding by ex- 
periment the absolute number of vibrations which may take place 

How are the major and the minor seventh severally produced ? 

Is it certain that the same string or other sonorous hody always yields 
under apparently similar circumstances the same number of vibrations? 

What musical note has been the object of particular attention in expe- 
riments on this subject? 

How near an agreement was found in respect to that note in the four 
orchestras at which it was examined ? 



250 ACOUSTICS. 

when the perception of any given tone or musical sound is pro- 
duced. Still the results obtained are valuable, as, by comparing 
them with calculations made on different grounds, measures of 
the ratios of sonorous vibrations may be deduced which seem de- 
serving of confidence. 

57. The number 426-f is nearly a mean between those derived 
from the observations made in the Parisian orchestras ; and by 
adopting it as that of the number of sonorous vibrations corre- 
sponding to the note A formed by the third string of the violin 
when open, the number 256 will be obtained as that representing 
the vibrations connected with middle C, or the sixth below A. 

/For since the vibrations of A are to those of C as 5 to 3, those of 
\the former being 426f in a second, those of the latter must be 
256 ; because, as 5 : 426f : : 3 : 256. Now this last number, being 
taken to represent the vibrations corresponding to the note C, 
marked in music by the tenor clef, the octaves in the descending 
or ascending scale will be denoted by numbers which are so many 
duplicate multiples of unity.* 

58. When an extended string is made to vibrate by striking it 
or drawing across it a violin-bow, it will yield a tone depending 
on its dimensions and tension ; but besides this, which may be 
called the fundamental tone, the string will, when the vibration is 
caused by striking it, emit not only its fundamental or proper note, 
but also other relative tones, especially the third and the fifth 
above the proper note. The co-existence of these relative tones 
with the principal one depends on the excitement of vibrations 
corresponding with the divisions of the string which would form 
the principal concords to the fundamental note. When the string 
is made to vibrate by means of a violin-bow the sound is simple 
and distinct, arising from the fundamental tone only. 

59. If a single string of a harp or pianaforte be struck, other 
strings of the same instrument tuned in fifths and thirds to the 
former will be thrown into the state of sonorous vibration, and as 
the original tone becomes weaker the relative tones or sympathetic 
concords will be more distinctly perceived. The effect produced 
on strings by the vibration of other strings near them, tuned so as 
to form concords, may be visibly demonstrated by placing small 
bits of paper bent in the form of the letter V inverted thus j± on 
one or more strings, so tuned as to yield tones an octave, a fifth, 

What open string of the violin corresponds to the note in question r 

What number of vibrations may we assume for its rate of vibration 
per second ? 

What will be the number for middle C of the piano ? 

How many times can we divide this number and its successive quotients 
by 2, before we arrive at 8, the lowest number of vibrations which Sa- 
vart found to produce audible sounds ? 

Can a string by a single stroke be made to yield more than a single 
tone ? 

Illustrate this position. 

* See Scale of Octaves, of this article, No. 57. 



VIBRATING PLATES. 



251 



or a third above a particular string; and, on causing the latter to 
vibrate strongly, the other strings will suffer corresponding vibra- 
tions, as will appear from the bits of paper falling off. Hence sin- 
gular effects are sometimes produced by the sympathetic influence 
of sonorous vibrations. 

60. An account of some remarkable experiments illustrative of 
the subject under discussion is given by J. B. du Hamel, a 
French philosopher of the seventeenth century ; which are the 
more deserving of notice, as they are circumstantially recorded. 
After observing that a glass cup or goblet may be broken by a 
man's voice, the writer adds, " First of all it is necessary that 
the tone which the glass is adapted to yield should be ascertained 
by ringing it, as may be done by giving it a slight fillip with the 
finger; then, the voice being accommodated to that tone and gra- 
dually augmented in loudness and raised to the octave above the 
original tone, the imperceptible minute particles of the glass 
shaken by reiterated concussions will be agitated with tremulous 
undulations, which, increasing by the continued operation of the 
concussions, will at length attain such force that the glass will 
fly in pieces. Some caution is necessary in the choice of a glass, 
which should be quite clean, free from any lines or flaws on the 
surface, and capable of yielding such a tone when struck, as the 
voice of the individual making the trial can easily reach." 

61. Another experiment exhibited at the same time or place is 
also thus described : "Two glass goblets are to be procured, into 
which water is to be poured to the depth of two or three inches, 
and they must then, by the addition of more water to one or the 
other as may be requisite, be made to yield the same tone when 
struck. This having been effected, if a small portion of bent wire 
be placed across the edge of one glass, then on rubbing the edge / 
of the other lightly with a wet finger, the sonorous vibrations thus 
excited will be communicated to the glass with the wire on its 
edge, and while sound is produced the light fragment of the wire 
will be seen dancing as it were to the music of the glasses."* 

62. The sonorous vibrations of plates or disks formed of elastic 
solids, as glass or metal, may be traced and rendered visible, by 
methods pointed out by Dr. Chladni, whose researches concerning , 
the doctrine of Acoustics have been referred to elsewhere. He 
ascertained that sounds might be elicited from plates of glass 



Oo what does the effect probably depend ? 

What occurs when a single string- of an instrument is struck ? 

How may this be made visible ? 

What remarkable effects of sympathetic vibration were obtained by Du 
Hamel ? 

In what manner does the experiment succeed with the greatest cer- 
tainty ? 

In what manner did Chladni operate to produce musical vibrations in 
elastic plates ? 

* J. R. tlu Hamel Onerum Philosoph., t. ii. Norimb.* 1GS1. 4to. pp. 
411, 565. 



252 ACOUSTICS. 

ground smooth on the edges, by drawing- the bow of a violin over 
any part of the edge of such a plate ; and that when sand had been 
y previously strewed over the surface of the plate, it would become 
arranged in certain lines according to the manner in which the 
plate was supported. M. Oersted, who repeated, with various 
modifications, the experiments of Chladni, ascribes the production 
of lines in sand, or any other light powder, as the dust of lycopo- 
dium, strewed on vibrating plates, to electricity.* 

63. Mr. Faraday has recently proposed a different explanation 
of these phenomena, which attributes them to the formation of 
currents in the air surrounding the vibrating plate which, pro- 
ceeding from the more fixed to the agitated parts of the plate, pass 
upwards and involve in their vortex any light particles of matter 
which they encounter. He showed that the current of air could 
be interrupted by walls of card, when the light particles took 
different directions. He observed that particles of heavy sub- 
stances, as sand, went to the lines of rest because the current of 
air was too weak to carry them in its course ; but that light bodies, 
as powder of lycopodium, being easily affected by the air in its 
motion, passed in a contrary direction. 

64. In confirmation of this view of the subject Mr. Faraday 
stated that when plates are made to vibrate in water instead of 
air the effect is different, particles of sand being then carried from 
the quiescent to the agitated parts of the plate, as the lighter par- 
ticles were in air ; and also, that when plates are made to vibrate 
in a vacuum, even the lightest particles pass to the lines of rest, 
there being no current of air to sweep them in the opposite direc- 
tion. j 

65. These peculiar figures formed on vibrating plates, though 
apparently resulting from simple causes, present sometimes singu- 
lar appearances. The arrangement of the lines of sand, or other 
substances, depends on the manner in which the vibrating plate 
is supported, and the point at which the violin-bow is struck against 
its border ; as also on the form of the plate, and other circumstan- 
ces already noticed. Some idea of the nature of these figures may 
be derived from the annexed representations ; the first figure being 
produced by holding a square plate of glass with a pair of tongs 
in the centre, and passing the bow over the middle of the edge at 

To what did Oersted attribute the formation of nodal lines in Chladni's 
experiments ? 

How did Mr. Faraday explain them? 

What occurs when plates vibrate in water ? 

What in the vacuum of an air-pump ? 

On what does the peculiar arrangement of sand on the vibrating plate, 
appear to depend ? 

What arrangement of lines will be given by a square plate held by the 
centre and rubbed with the violin-bow in the middle of one edge ? 

* See Nicholson's Journal of Natural Philosophy. Svo. vol. x. p. 256. 
t Arcana of Science, 1832, p. 77 ; from Journal, edited at the Royal 
Institution. 



MUSICAL INSTRUMENTS. 253. 

either side ; and the other arrangements depend on the shape ot 
the plate and the mode of striking it. 





66. It is in consequence of the resonances or sympathetic propa- 
gation of sounds, that in a large apartment, tones are sometimes 
emitted from the walls, floor, ceiling, or furniture ; owing to the 
excitement occasioned by the tone of an instrument or a man's 
voice acting on some object adapted to yield a tone in concord 
with the original tone. It may even be observed that one part of 
a floor or any other surface will be thrown into the state of sonor- 
ous vibration by one sound, and another by a different sound ; and 
the tremulous motions thus produced in various objects may be 
perceived by the sense of touch. 

67. The ancient Romans were well acquainted with the doctrine 
of resonances, and availed themselves of their knowledge in order 
to facilitate the propagation of sound through their theatres. The 
method they adopted was to inclose in the walls of those build- 
ings hollow globular vessels, so fixed as to be excited into sonor- 
ous vibration by the voices of the actors, and thus add considera- 
bly to their effect. 

98. Musical instruments, how much soever the}^ may differ one 
from another as to the mechanical modes by means of which they 
are made to produce soniferous vibrations, have one common pro- 
perty, namely, that they all yield the same tone relatively to the 
numbers of their vibrations. Hence the term concert pitch, or the 
sound of a fundamental note corresponding to a certain number of 
vibrations performed in a given time by the sonorous parts of 
several instruments which are to be used in conjunction. Differ- 
ent methods are adopted by musicians for obtaining an invariable 
tone, from which they may compare and regulate any number of 
instruments to be used in concert; and the tone of this note being 
decided, they proceed to adjust the strings of violins, violoncellos, 
and other such-like instruments, so that they may all correspond 
with each other, as well as with those instruments which by their 
construction are fitted to yield permanent tones. This operation 
is called tuning, or putting instruments in tune. 

69. Sometimes the fundamental tone is ascertained by means 

What occasions the emission of tones from the walls, floors, and fui • 
future of an apartment ? 

What advantage was taken of this principle by the ancient Romans? 

What common property have all musical instruments ? 

What is meant by the term concert pitch ? 

What three methods are employed by musicians to get the invariable 
tone, or concert pitch ? 

Y 



254 ACOUSTICS. 

of a pitch-pipe, which consists of a tube capable of being length > 
ened or shortened at pleasure by the introduction of a moveable 
plug; so that by blowing into it at the mouth-piece, either of the 
notes of the gamut may be produced. Another instrument for 
obtaining fixed and determined tones is the monochord,* which 
is merely a string or wire of given length and diameter, the ten- 
sion of which may be regulated by certain weights hanging from 
one end, while the body of the string passes over two bridges or 
other solid supports, and the other end is nrmh r secured. 

70. But the most usual instrument employed by musicians as 
the index of a fundamental tone is that styled the tuning-fork. It 
is a steel rod curved nearly into the figure of a sugar-tongs, but 
having a short handle fixed to the convex side of the curved part, 
and terminating in a knob : it may be made to yield sonorous 
vibrations, if it be held by the handle so as to leave the prongs 
free, and, after striking one of the prongs smartly against the edge 
of a table or any other solid body, setting the knob against the 
table. The sound or tone emitted must depend on the dimensions 
of the rod or its prongs : those that are used for tuning pianofortes 
or harpsichords yielding the tone called middle C ; and other tun- 
ing-forks giving the sixth above it, or A, the note which ought to 
be produced by the third open string of the violin, whence the 
other strings of that instrument are adjusted."}" 

71. Instruments of music may be arranged in classes, according 
to their forms or modes of action. It will be sufficient here to 
distinguish them into stringed instruments ; pulsatory instruments 
including bells, drums, &c. ; those in which sound depends on the 
vibrations of elastic rods, hemispheres, or plates ; and wind in- 
struments. The varieties of the first and the last of these classes 
are extremely numerous ; and many of them were invented at a very 
early period. It has been questioned which of the two may be 
justly reckoned the most ancient. A recent ingenious writer 
seems inclined to decide in favour of stringed instruments. He 
says, " The lyre or harp is surely as ancient as any instrument on 
record. The mythologist ascribes the idea of producing sound by 
the vibration of a string to Apollo ; which is said by Censorinus 
to have suggested itself to him on his hearing the tw~ang of the 
bow of his sister Diana.":}: 

72. Among the principal varieties of stringed instruments are 
the violin, tenor, violoncello, and double bass, in all which the 

What is the construction of the monocbord ? 
Into what four classes are musical instruments distinguishahle f 
Which classes present the greatest variety ? 

On what circumstance in the action of stringed instruments/does the 
performer chiefly rely for the extension of their range of notes? 

* From the Greek MSvo?, one ; and Xop5>, a chord, or string. 

t"The tuning-forks of different nations give different tones for the 
same letter. A London and a Vienna A fork have sometimes been found 
about one-third of a note apart. — Ed. 

$ Philosophy in Sport made Science in Earnest, edit. 1833, p. 300. 



PULSATORY INSTRUMENTS. 255 

relative gravity or acuteness of the tones they emit depends partly 
on the tension and diameter of the strings, and partly on their 
lengths, which are regulated by stopping them in certain parts 
successively by the application of the fingers, principally near 
the neck of the instrument, while the stopped or open string, as 
may happen, is made to vibrate by drawing across it a bow 
armed with horsehair. As more than one string may be put into 
the 9tate of sonorous vibration at one time, harmony or music 
in parts, as well as melody, may be elicited from the violin and 
similar instruments. 

73. In the hands of skilful performers the violin exhibits unri- 
valled powers ; as those who have witnessed the magical execu- 
tion of Paganini, will in general be readily disposed to admit. 
Those who have never heard him may acquire some faint idea of 
his extraordinary skill, from the circumstance of his being able to 
produce abundance of excellent music from his instrument, after 
having made a monochord of it, by taking away all the strings 
except one. 

74. The guitar somewhat resembles the violin in figure and 
construction, but it is played on usually by twitching the strings 
with the fingers, and a variety of notes may be produced by stop- 
ping the strings with the left hand, so as' to regulate the numbers 
of their vibrations and consequent tones. The performer gener- 
ally uses the guitar to furnish an accompaniment to the voice: its 
power alone being inconsiderable. The harp is likewise played 
on with the fingers, but its strings are numerous and all open. 
The pianoforte and the harpsichord have also distinct strings for 
each tone and semi-tone ; and like the harp they are adapted for 
the performance of music in parts ; so that they may serve either 
for playing symphonies or other pieces of music wholly instru- 
mental, or for accompaniments to the voice. 

75. Pulsatory instruments of music display considerable varie- 
ties of form, comprising the double drum, the opposite ends of 
which yield different tones when struck, for the parchment cover- 
ing one extremity is, by regulating its relative degree of tension, 
made to yield a sound which is a fifth in tone different from that 
of the other extremity; kettle-drums consisting of copper hemis- 
pheres, the open ends of which are covered with parchment, and 
two such drums properly tuned being used, they may be intro- 
duced instead of a double drum, but will be distinguished by a pe- 
culiarity of intonation, though yielding the same notes ; the tam- 
bourine, a well-known instrument, resembling in principle the 
preceding ; besides some others of a similar nature. 

What remarkable fact proves the power of the violin ? 

In what chief circumstance does the guitar differ from the violin ? 

For what purpose is it generally employed ? 

Are the strings of the harp, pianoforte, and harpsichord capable of 
being varied in tone by alterations of length at the pleasure of the per- 
tormer ? 

Enumerate some of the chief pulsatory instruments.* 



256 ACOUSTICS. 

76. Bells, gongs, &c, are open hemispheres, or conical instru- 
ments made of some sonorous metals : the latter of which, used 
in China, are large and very powerful instruments. Among re- 
cently-invented musical instruments is one called the Harmonicon, 
constructed by ranging in one or more lines a number of small 
oblong disks of glass, each adapted, by its vibrations when struck, 
to yield one of the notes of the gamut or common musical scale, 
including two or more octaves according to the size of the instru- 
ment: the disks are fixed securely at one end only, so that they 
vibrate freely on striking them with a hammer much like the ham- 
mers of a pianoforte. 

77. Glass hemispheres or bell-shaped goblets, fixed in a frame, 
and tuned to the gamut, by pouring in more or less water, form 
an agreeable instrument of music, played on by striking the edges 
with a violin-bow, or by being thrown into the state of sonorous 
vibration by gently touching them with wet fingers. There are 
several varieties of these instruments, which, as well as the pre- 
ceding, have received the names of harmonica, and harmonic 
glasses. 

78. Wind instruments display no less variety in their construc- 
tion and mode of action than stringed instruments ; and in the 
opinion of some antiquaries they were invented at a more remote 
period than the latter. The general principle they involve is 
that of the production of sounds by the vibrations of columns of 
air, usually contained in tubes, whose relative lengths and those 
of the included columns determine the numbers of the synchronous 
waves or vibrations to which the tones or musical sounds emitted 
owe their character as to gravity or acuteness. 

79. Instruments of this class have been distributed into three 
kinds: (1.) those in which the contained column of air is made 
to vibrate by blowing forcibly into one end of an open tube; (2.) 
those in which the vibration of the air is caused by blowing 
through a solid mouth-piece, at one end, which merely limits the 
size and figure of the aperture, and thus adds to the force with 
which the air is introduced through it; (3.) wind instruments 
played on with a reed or very elastic mouth-piece, the primary vi- 
brations of which highly augment the sonorous vibrations of the 
column of air. 

80. There is likewise a distinction to be made between tubes 
open at both ends, without any lateral apertures, and those which 
nave several such apertures, the obvious effect of which must be 
to lengthen or shorten the tube, or rather the column of air in it, 

To what nation is the gong chiefly confined ? 

How are harmonica constructed ? 

In what manner may the tones of musical glasses be varied so as to tune 
an instrument constructed of them ? 

What circumstance determines the gravity or acuteness of tones given 
by tubes in wind instruments? 

Into how many and what classes are instruments of this nature distin- 
guishable ? 



WIND INSTRUMENTS. 257 

on the dimensions of which the sonorous vibrations and concomi- 
tant sounds must depend. 

81. Among- the first mentioned species of wind instruments 
must be included the trumpet, the bug-le-horn, the French-horn, 
Pan's pipes, and some others, which however they may differ in 
form, or in the effect of the tones they yield, are all made to sound 
by blowing- through a circular aperture ; and from these the Ger- 
man flute is distinguished merely by having the aperture through 
which air is admitted in the side of the tube, while the end 
is closed. To the second species of instruments belongs the 
flagelet, which is played on by means of an ivory mouth-pieCe, 
having an aperture of invariable dimensions. The third species 
of wind instruments comprehends several varieties, some having 
mouth-pieces possessing a slight degree of flexibility, as the cla- 
rionet; others are played on with a reed, forming a highly flexi- 
ble mouth-piece, as the hautboy and the bassoon. The diversity 
of sounds produced by different sets of organ-pipes,' answering to 
the respective stops of the instrument, depend on the peculiar 
forms of the pipes, and especially on the manner in which the 
air is admitted into them. 

82. The Jew's-harp, an instrument too generally known to need 
description, and commonly despised as utterly insignificant and 
inharmonious, is however deserving of particular notice, not only 
as being a wind instrument affording sounds on somewhat diffe- 
rent principles from those above described, but likewise because, 
in the hands of more than one performer, it has been found capa- 
ble of producing considerable effect, and exciting the admiration 
of musical amateurs. As the Jew's-harp has no cavity it is al- 
most inaudible when struck, till it is placed between the lips and 
teeth of the performer, and thus the sonorous vibrations on which 
its tones depend are formed in the mouth, the tongue or bent wire 
belonging to the instrument acting the part of a reed. 

83. Three tones or notes only can be produced by means of a 
single harp ; the lowest of which may be termed its fundamental 
note, and the others are its principal concords the third and fifth. 
From a scale so limited it would be impossible to derive melody, 
much less harmony ; and therefore the instrument was neglected 
by regular musicians, though commonly used among the peasantry 
in many parts of Europe, and particularly in the Netherlands and 
in the Tyrol. Some kind of improvement was effected by the 
Tyrolese, by uniting two Jew's-harps, or using two at once ; and 
this method was adopted by a Prussian soldier, mentioned in the 
Memoirs of Madame de Genlis, as having acquired the art of play- 

What is the purpose of the holes usually seen in instruments of this 
sort ? 

Give examples of each of the three classes of wind instruments. 
On what do the different tones of organ-stops depend ? 
What is necessary to the production of sound by the Jew's-harp ? 
What is its range of scale, and what the notes it can actually yield? 
13y whom has it been extended and improved ? 
Y 2 



258 ACOUSTICS. 

ing on this instrument with so much skill and taste that he was 
heard with pleasure and surprise by the king, Frederic the Great, 
who possessed considerable knowledge of music, and was him- 
self a good performer on the German flute. 

84. But to the more recent labours of M. Eulenstein we are in- 
debted for the complete developement of the powers of this little 
iustrument. He devoted ten years to the study of its capabilities, 
and the means of removing its defects ; and having ascertained 
the compass of tones belonging to it, as stated above, he conceiv- 
ed the idea of extending its power, and supplying the intervals 
wanting, so as to complete the gamut through several octaves, by 
joining sixteen Jew's-harps, aud then tuning them by fixing more 
or less sealing-wax at the extremity of the tongue. By means of 
this construction he effected his object, a? by rapidly changing 
from one harp to another, he could elicit any series of tones, and 
perform pieces of music, in a manner which delighted and asto- 
nished those Who heard him. 

85. It appears both from theory and experiment, that in the fun- 
damental sound of a tube open at both ends, the portions of the 
included column of air on the opposite sides of the centre of the 
tube move in directions contrary to each other. This principle is 
ingeniously confirmed and illustrated by Mr. Wheatstone, in a 
paper read before the Royal Institution of London, March 16, 
1832 ; when he exhibited the phenomenon in question, by means 
of an apparatus consisting of a leaden tube about an inch in dia- 
meter and thirteen inches long, bent nearly into a circle, so that 
its two extremities might be opposite to each other, with a small 
space between them. Within this space, equidistant from each 
end of the tube, was held the vibrating part of a square plate of 
glass thrown into a state of vibration, either by means of a violin- 
bow, or a hammer, so as to produce its lowest sound, or that de- 
noted by Chladni's first figure. By this arrangement, the plate 
advancing in its vibration towards one end of the tube, and re- 
ceding at the same instant from the other, the effects neutralize 
each other, and no resonance, or augmentation of the original 
sound takes place. In the middle of the tube was a joint, which 
allowed either half to move independently round the axis of the 
tube ; and thus the two ends could be brought to the opposite 
sides of portions of the plate which were vibrating at the same 
moment on contrary sides of the neutral plane : in this case the 
impulses were made at the same instant towards each end of the 
tube, and the augmentation of sound was considerable.* Hence 

What remarkable attention has been bestowed on the developement of 
its powers ? 

How did Eulenstein tune his instrument ? 

What appears to be the kind of motion which takes place in the co- 
lumn of air within a tube open at both ends ? 

Describe Wheatstone's method of exhibiting this principle. 

* Report of British Association, p. 556. 



VIBRATION OF COLUMNS OF AIR. 250 

it appears that in a tube or pipe, open at both ends, the vibrating 
column will be double, and therefore only half the length of that 
in a similar tube closed at one end ; so that the latter would yield 
a tone an octave lower than the former. 

86. Mr. Wheatstone investigated the modes of vibration of co- 
lumns of air in conical tubes, and ascertained that the air in a tube 
of this form, excited into vibration at its closed end, or at the sum- 
mit of the cone, yielded the same fundamental sound, and the 
same series of harmonics as a cylindrical tube open at both ends. 
Thus he showed that the trumpet, French-horn, and hautboy pipes 
of the organ, all being conical pipes, produced the same sounds 
as the cremona pipe, a cylindrical tube, excited in the same man- 
ner, and only half their length. He likewise compared the haut- 
boy, a conical tube, with the clarionet, a cylindrical tube of the 
same length,* and demonstrated that in the former the fundamen- 
tal sounds were the same, absolutely and relatively, as in the 
flute, a tube of the same length, open at both ends ; and that in 
the latter the fundamental sounds were relatively as those of a 
tube of similar length closed at one end. 

87. A tube or pipe, the upper aperture or mouth-piece of which 
is placed close to the lips, as in the case of the trumpet, French- 
horn, or clarionet, is to be considered as open at the lower end 
only; and thus its tones are relatively deeper and more powerful 
than those of the German flute or flagelet, tubes open at both ends ; 
for the aperture through which the flute is blown or made to 
sound, is not covered by the lips of the performer; and though 
the mouth-piece of the flagelet is covered in playing on that in- 
strument, it is reduced to the state of a tube open at both ends, 
in consequence of its having a lateral aperture near the upper ex- 
tremity. 

88. The theory of musical sounds may be elucidated from the 
consideration of the manner in which tones are produced from the 
French-horn. As the harmonics or concords of a fundamental 
note may be obtained by the division of a vibrating string into 
certain proportions, so the same series of tones may be formed by 
the spontaneous division and subdivision of the column of air con- 
tained in the French-horn. When this instrument is used in con- 
cert, it must always be adjusted to a certain length, by increasing 
or diminishing the number of the cranks, or circular tubes of which 
it is composed ; so that the gravest tone it will yield may corre- 
spond with the key-note or fundamental tone of the piece of music 

To what result did his investigation lead ? 

What relation has the tone of a conical to that of a cylindrical tube of 
the same length ? 

How is a tube or pipe to be regarded when the mouth-piece fits close 
to the lips ? 

How is the French-horn adjusted to a particular concert-pitch ? 

Which of its notes ought to be adjusted to the key-note ? 

* The bell-shaped part of the clarionet has no effect on its tone. 



260 ACOUSTICS. 

to be performed. Suppose this tone to be C, if then the horn, 
properly adjusted, is blown gently, this note will be heard ; a 
stronger blast will double the number of the sonorous vibrations, 
and produce an octave above the first note ; by increasing the force 
of the blast may be obtained in an ascending series a fifth, then 
an octave above the second C ; then a third, a fifth, and an octave 
above the third C ; then a fourth octave, including nearly all the 
tones of the common musical scale. 

89. Thus in the French-horn, the common bugle-horn, and 
other instruments formed on the same plan, the different tones are 
produced by varying the impulse given to the included column of 
air in blowing them ; while in such instruments as the German 
flute, the same effect is more perfectly obtained by altering the 
length of the vibrating column, which is done with the requisite 
ease and rapidity by the apertures alternately opened and closed 
by means of the fingers or keys. 

90. The iEolian harp, in point of construction, is a stringed 
instrument, but its sonorous vibrations are caused by the impulse 
of the air ; and its tones may be characterized as the music of 
nature improved by art. It usually consists of an oblong deal 
box, four or five inches high, and adapted to the aperture formed 
by nearly closing a sash window, so that the current of air passing 
through the opening may sweep over wires or harp-strings, ex- 
tended lengthwise upon the top of the box, in which there must 
be sound-holes like those of a violin, and the wires are to be 
supported and stretched by a bridge at either end. Four strings 
or wires may be tuned so that the third may be an octavo above 
the first, the second a fifth above the first, and the fourth a fifth 
above the second. But various arrangements may be adopted, in 
consequence of any of which, alternately increasing or diminish- 
ing strains of wild harmony will be elicited from the instrument 
by the fluctuating impulse of the wind. 

91. A colossal imitation of the instrument just described was 
invented at Milan in 1786, by the Abbate Gattoni. He stretched 
seven strong iron wires, tuned to the notes of the gamut, from 
the top of a tower fifty feet high to the house of a Signor Mos- 
cati, who was interested in the success of the experiment; and 
this apparatus, called the Giant's Harp, in blowing weather, 
yielded lengthened peals of harmonious music, now swelling in 
loud chorus, and seeming to fill the atmosphere, then dying away 
on the breeze like the soft tremulous murmurs of a common JEo- 
lian harp. In a storm this aerial music was sometimes heard at 
the distance of several miles. 

What will enable the performer to increase the acuteness of the tone 
to an octave ? 

In what manner does the mode of varying the acuteness of sound in 
the common bugle differ from that in the German flute ? 

What is the common construction and mode of applying the iEolian 
harp ? 

What account is given of a remarkable instrument of this construc- 
tion ? 



VIBRATIONS OF INSECTS. 261 

92. The music of nature exhibits boundless variety as to the 
combinations of tones and the several modes in which they are 
produced. But besides the warblings of the feathered choir and 
abundance of other vocal sounds with which we are familiarly 
acquainted, there are some which are constantly emitted under 
certain circumstances, yet, though curious and interesting, they 
seldom attract our notice. 

93. Bees, gnats, and many other winged insects in their pas- 
sage through air excite sonorous vibrations by the viewless 
flutterings of their wings or other membranous parts of their 
structure. The intermitting note of the grasshopper is probably 
the result of a similar mechanism ; but some insects of this tribe 
seem to be furnished with a peculiar organization for the pro- 
duction of their music. 

94. Dr. Hildreth states that the American Cicadas, or locusts, 
are furnished with bagpipes on which they play a variety of notes. 
" When any one passes they make a great noise and screaming 
with their air-bladder or bagpipes. These bags are placed under 
and rather behind the wings, in the axilla, and something in the 
manner of using the bagpipes, with the bags under the arms. I 
could compare them to nothing else ; and indeed I suspect the 
first inventor of the instrument borrowed his ideas from some in- 
sect of this kind. They play a variety of notes and sounds, one 
of which nearly imitates the scream of the tree-toad." 

95. Some birds yield musical tones through the percussion of 
the air by their wings in flight. This circumstance, which per- 
haps has escaped the attention of naturalists, is particularly ob- 
servable in the lapwing, or as it is sometimes called from its cry, 
the pewit. This bird is an inhabitant of the furze-clad downs of 
Wiltshire; and when it stoops near the ground, in its circling 
course through the air, as it approaches the observer, a sound may 
be heard resembling the distant tone of a French-horn, entirely 
distinct from the dissyllabic scream from which it derives its 
provincial name ; and which is formed like the cries of other ani- 
mals in the throat or larynx. The peculiar clanging tone first 
mentioned seemed, as far as could be guessed from repeated ob- 
servations, to be nearly the same note with the middle C of the 
harpsichord. It is manifestly caused by the reverberation of the 
air against the hollow sides of the broad wings of the bird in its 
rapid wheeling flight ; and it is heard only when it happens to 
come very near the observer.* 

How are winged insects generally found to produce sound ? 
How is the American locust furni hed with musical instruments ? 
By what means other than the voice are birds sometimes found to give 
musical tones ? 

* The common night-hawk affords a familiar illustration of the effect 
of rapid stooping through the air, producing the " boo-oo" often heard on 
a warm summer evening. — Ed. 



262 ACOUSTICS. 



The Human Voice. 

96. Among the most curious works of nature, must be reck- 
oned the organization on which depend the tones of the human 
voice. The most ancient physiologists regarded the trachea or 
windpipe as the immediate organ of sound, comparing it to a flute, 
and ascribing the voice to the impulse of air against its sides in 
its passage into the lungs. But Galen controverted this erro- 
neous opinion, by showing that the voice is formed during the 
expiration of air, or its passage from the lungs, and in its es- 
cape from the larynx, at the back of the mouth. Besides the 
lungs, which propel air in the same manner as it is propelled by 
a bellows into the pipes of an organ, the parts essential to the 
production of vocal sounds are the trachea or windpipe, the larynx, 
and its appendages. 

97. The windpipe, as the term implies, is merely a cartilagi- 
nous canal through which the air issues from the lungs; the 
larynx is an enlarged continuation of the windpipe, formed, like 
it, of cartilage or gristle, membrane and muscle; but it is more 
complicated, terminating above in two lateral membranes, which 
approach near together, leaving only an oblong narrow opening, 
called the glottis. The cartilages of the larynx admitting of some 
degree of motion by means of their attached muscles, the mem- 
branes of the glottis, which are connected with them, may be 
extended or slackened, and thus the vibrations of the air passing 
through the glottis are regulated, and sounds are modified as to 
tone. Tendinous cords or ligaments are also extended within 
the larynx, which are supposed by some physiologists to co- 
operate with the membranes of the glottis in producing sonorous 
vibrations. 

98. The glottis, or rather the membranes which compose it, 
thus appears to form the immediate organ of sound ; which has 
been aptly enough compared to the reed of a hautboy, since . is 
composed of thin vibrating plates, with a narrow variable ope ,ing 
between them. But the surpassing delicacy of the organization 
in the construction of the glottis abundantly demonstrates the 
superiority of the works of nature over the most elaborate efforts 
of art. Dodart, a French physician, who, in the beginning of the 
last century, investigated the structure of the vocal organs, made 
a calculation whence he inferred that the intervals of sound capa- 
ble of being perceived by the ear correspond to contractions of 
the glottis less than 1-9632 part of its diameter. It is probable, 
however, that the diversity of tones is caused not merely by alte- 

What part of the organs of speech did the ancients regard as the im- 
mediate cause of sound ? 

Who controverted this opinion, and on what ground ? 

What, besides the windpipe, is essential to the production of vocal ut- 
terance ? 

What is meant by the larynx? what, by the glottis? 

What office does the glottis appear to perform ? 



ORGANS OF SPEECH. 263 

rations in the dimensions of the glottis, but is parti 3 r dependant on 
the lengthening' or shortening of the entire tube of the trachea, in- 
eluding the larynx, and by corresponding alterations in the form 
and size of the cavity of the mouth. Yet the power of varying 
the tones of the voice in singing must depend chiefly on the sus- 
ceptibility of the membranes of the glottis, the firmness and elas- 
ticity of the cartilages of the larynx, and the strength of the mus 
cles by which they are moved, and that of the muscles of the ches 
concerned in respiration. 

99. That the sound of the voice wholly arises from the pas- 
sage of air from the lungs through the glottis, is proved by the 
fact that when the windpipe is wounded below the glottis so that 
the air in expiration passes through the wound, the power of 
forming sounds is destroyed; while a wound in the throat which 
leaves the glottis and parts below it uninjured, produces but little 
effect on the voice; and if a piece be cut out of the windpipe of a 
man or any animal similarly constituted, the power of uttering 
sounds of which he is thus deprived will be restored by carefully 
closing the artificial opening in the windpipe, so that the air no 
longer escaping by it, may pass through the glottis as usual. 
Hence those unfortunate persons who cut their own throats so as 
to wound the windpipe but not the large blood-vessels, imme- 
diately breathe through the wound and become silent, but as soon 
as the wound is dressed and the air no longer passes through it, 
the power of speaking is restored. 

100. The tracheal canal, including the larynx, may even be 
entirely detached from the animal to which it belongs with- 
out losing its property as a vocal instrument. The celebrated 
naturalist Cuvier, having cut off the head of a screaming bird so 
as to leave the glottis and parts below it entire, the creature still 
uttered cries for some time after its decapitation, the organ of 
voice remaining uninjured. An animal recently dead may be 
made to utter sounds as when living, as appears from experi- 
ments made by M. Ferrein, in 1741, and repeated by M. Biot, a 
few years since. The latter gentleman employed in his researches 
the larynx of a pig, with the trachea attached to it, and to the 
opening of the latter, he fitted the bellows of an organ, and by 
varying pressure on the larynx with his hand he could increase 
or diminish the aperture of the glottis while forcing the air through 
it, so as to imitate exactly the grunting of the pig. The same 
philosopher subsequently constructed an artificial glottis, the 
lamina, or membranous plates forming the opening being made 



On what operations besides the enlargement and contraction of the 
glottis is variety of tone supposed to depend ? 

What direct proof have we that the voice is formed at the glottis r 

What experiment did the celebrated naturalist Cuvier institute on this 
subject ? 

In what manner did Biot imitate the voice of the living animal ? 



264 ACOUSTICS. 

of gum elastic; and having adapted it to the pipe of a pair of bel- 
lows, he was thus enabled to produce vocal sounds.* 

101. The aperture of the glottis is naturally more contracted in 
females and in males before the age of puberty, than in adult 
males ; and therefore, women and children have shriller voices 
than men, the difference of tone commonl3 r amounting to about 
an octave. The entire compass of voice in female singers is usu- 
ally more extensive than in men; for though their scale of musi- 
cal sounds commences at a relatively high tone, it ascends yet 
higher in proportion. 

102. The human voice may be so modulated as to form a vast 
variety of* musical sounds or tones with rapidity and precision far 
beyond the effect of any instrument formed by art ; for vocal mu- 
sic, on account of its superiority over instrumental music, in point 
of expression, must always be regarded as the highest excellence 
of the art. But the vocal organs not only afford tones or sounds 
distinguished by relative gravity or acuteness, but also modifica- 
tions of sound, forming the basis of language ; and to the posses- 
sion of the faculty of speech, and the interchange of vocal and 
audible signs, man is greatly indebted for his superiority over the 
brute creation. 

103. It is during the transmission of the sonorous vibrations 
through the mouth that the peculiar effect is produced which com- 
municates to the ear the sounds of letters and words, constituting 
language. The most simple of these articulate sounds are those 
corresponding with the vowels, the differences between which 
depend on enlarging or contracting the cavity of the mouth while 
they are uttered. The consonants, which, it hardly need be ob- 
served, cannot be enunciated without the addition of a vowel, 
require more complicated motions of the parts of the mouth; and 
hence some of them are called gutturals, as being formed in the 
back part of the mouth; some dentals, as requiring the application 
of the tongue to the teeth; and others labials, because the}' cannot 
be distinctly pronounced without moving the lips. 

104. The success of the researches of men of science concern- 
ing the theory of vocal intonation has occasioned different attempts 
to produce speaking machines, the operation of which should de- 
pend wholly on mechanism. In 1779, a prize was offered by the 
Academy of Sciences at St. Petersburg, for the best dissertation 
on the theory of vowel sounds, illustrated by actual experiments; 
and it was awarded to G. R. Kratzenstein, an account of whose 

How is the opening of the glottis in females compared with that in 
males ? To what amount do they generally differ ? 

How is the human voice, in point of variety and rapidity of execution, 
compared with musical instruments ? 

On what condition of the vocal organs do the different vowel sounds 
depend } On what three parts of the mouth are the consonant sounds of 
language mainly dependent? 

* V. Sigaud de la Fond Elem. de Phys., vol. iii. p. 551; Teyssedre 
Elem. de Phys., p. 214. 



F0R3IATI0N OF VOCAL SOUNDS BY MECHANISM. 



265 



researches was published in the Transactions of the Academy. 
This igenious philosopher showed that the sounds of the four 
vowels, A, E, O, and U, might be obtained by blowing through 
a reed into several tubes, the forms of which are represented in 
the annexed figures 1, 2, 3, and 4 ; and that the sound of I, as 
pronounced by the French and other continental nations was pro- 
duced by blowing at cr, into the pipe No, 5, without using a reed. 
Kratzenstein continued his investigations, but probably he did not 
obtain results of greater importance, as he never published any 
further account of the progress of his inquiries. 

3 4 <5 





105. M. Kempelen, of Vienna, who distinguished himself by 
the construction of an automaton chess-pla}^, which has excited 
much attention, also devoted his ingenuity to the contrivance of a 
speaking machine. He succeeded so far as to produce an instru- 
ment capable of uttering certain words and short phrases in French 
and Latin. The sounds appear to have been produced by mean* 
of a single cavity, the form and dimensions of which might be 
modified at pleasure. It has been described as consisting of a 
box, about three feet long, placed on a table and covered with a. 
cloth, under which the operator in exhibiting its powers introduced 
both his hands, one of which probably was employed in pressing 
on keys which might communicate with pipes after the manner 
of those of an organ. This machine was only shown to the pri- 
vate friends of the inventor, and it does not appear that it was ever 
completed.* 

106. A gentleman of Cambridge, England, has more recently 
prosecuted experiments on the formation of articulate sounds ; and 
having adopted the method of Kempelen, in using a single cavity, 
he found that by blowing through a reed into a conical cavity the 
vowel sounds could be produced by altering the dimensions of the 
aperture for the passage of air from the cavity by means of a 
sliding board. He also found that when cylindrical tubes, the 
length of which could be varied by sliding joints, were adapted 
to the reed, the series of vowels could be produced by gradually 
lengthening the tube ; and when its length was augmented in a 

Give some account of Kratzenstein's vocal pipes. 

To what extent did Kempelen, the inventor of Maelzel's automaton 
chess-player, carry the imitation of human speech ? 
Of what did his speaking machine consist ? 

* See Nicholson's British Encyclopaedia, art. Androides ; Brewster's 
Edinburgh Encyclopaedia, art. Automaton. 

z 



266 ACOUSTICS. 

certain proportion the same vowels were repeated but in inverted 
order ; and by a further augmentation of the length of the pipe, a 
second repetition of the vowels took place in direct order. 

107. The degree of accuracy with which some birds, and espe- 
cially parrots imitate the human voice, depends more on their 
propensity to mimic the sounds they hear than on any peculiar 
qualifications they possess for giving utterance to articulate tones ; 
and therefore many other animals, beasts as well as birds, 
might be taught to speak by any one who was disposed to bestow 
sufficient time and labour on such a task. Pliny the Elder men- 
tions certain nightingales, which spoke Latin and Greek;* but, as 
the authority of that ancient writer may be considered as some- 
what dubious, it will be more to the purpose to observe, that 
Father Pardies, a learned Jesuit, gravely asserts that dogs had 
been taught music, and that one of them was so apt a scholar, 
that he could sing a duet with his master. The celebrated phi- 
losopher Leibnitz has given an account of a dog which he saw 

/and heard speak, after it had been under tuition three years. This 

* animal could pronounce thirty words, such as tea, coffee, chocolate ,• 

and he merely repeated them after hearing them from his master, j- 

Reflection of Sound. 

108. When sonorous vibrations are propagated through a mass 
of matter of great extent, and of. uniform density and elasticity, 
as when they are continued uninterruptedly through the open 
air, the sounds will be heard alike in every direction, and become 
dissipated or lost in the surrounding space. But if they impinge 
on some obstacle which interrupts their progress, they will be 
driven back or reflected ; and thus a wall, the face of a rocky cliff, 
the surface of water, or even a dense body of vapour, may cause 
the reverberation of sound. 

109. The reflection of sound takes place ac- 
cording to the same laws that govern the re- 
flection of perfectly elastic solids. Hence the 
sonorous vibrations being propagated in right 
lines, the angle of reflection is always equal 
to the angle of incidence. Thus suppose a 
sound to be emitted from A in the annexed 
figure, and to impinge on a dense plane, E B 
F at B, it will return in the same line B A, and 
the reflected sound will be heard at A after the 

Wnac was found to be the effect on the vowel sounds of lengthening; 
speaking tubes ? On what is the imitative faculty of parrots dependent"? 
What is asserted by Pliny in regard to nightingales } What statements 
are mentioned of this power in quadrupeds? What is meant by the 
reflection of sound ? According to what laws does it take place ? 

* Plinii Histor. Natur., lib.x. cap. 42. 

t Histoire Critique de l'Ame des Betes. Amsterd. 1749. t. ii. p. 50. 
De la Connoissance des Betes, p. 129. Histoire de l'Academie des Sci- 
ences. An. 1715. p. 3. 




ECHOES. 267 

original sound, constituting what is termed an echo.* If, however, 
the sound he emitted from D, so that the line of its direction may- 
form an oblique angle with the plane E F, it will be reflected from 
B in the line B C, forming a similar oblique angle with the plane 
E F. The velocity of the reflected sound is precisely the same 
with that of the direct sound; therefore the sound will be returned 
from B to C in the same time that it passes from D to B. Hence 
the sound uttered at D will be heard by a person stationed at C at 
the end of a period double that which it takes to pass from D to 
B. So that as sound travels at the rate of 1130 feet in a second, 
if the distance from D to B should be 282^ feet, the echo will be^V 
heard at C in half a second, for in that time the sound would be 
conveyed 282^ X 2 = 565 feet. 

110. It is requisite that the reflecting body should be situated 
at such a distance from the source of sound that the interval be- 
tween the perception of the original and the reflected sounds may 
be sufficient to prevent them from being blended together. When 
they become thus combined the effect is termed a resonance, and 
not an echo. The shortest interval sufficient to render sounds 
distinctly appreciable by the ear is about 1-10 of a second ; 
therefore when sounds follow at shorter intervals they will form a 
resonance instead of an echo. So that no reflecting surface will 
produce a distinct echo unless its distance from the spot whence 
the sound proceeds should be at least 56<j feet, as the sound will 
in its progress forward and return through double that distance, 
113 feet, take up 1-10 of a second. Resonances, or combinations 
of direct and reflected sounds are heard more or less in all inclosed 
places of moderate extent ; and as they occasion some degree of 
confusion in the perception of sound, inconvenience arises from 
this source in rooms appropriated to the purposes of oratory, the 
voice of a speaker being heard but indistinctly, especially in some 
situations ; but in a concert-room such resonances are rather ad- 
vantageous, at least they would add to the effect of instrumental 
music. 

111. Some echoes will repeat but one syllable or distinct sound, 
while others will repeat several in succession. Hence the dis- 
tinction of monosyllabic and polysyllabic echoes. As it would 

Construct and explain the diagram relating to this subject ? 

What is meant by the angle of incidence of sound ? 

What by the angle of reflection ? 

What is the relation of those angles to each other? 

What are the comparative velocities of original and of reflected sound ? 

What name is given to the intermingling of original and reflected 
sound ? 

How far must a reflecting surface be placed from the source of sound, 
in order that an echo should be distinctly heard ? 

What disadvantage is occasioned by resonance? 

In what cases may it be found beneficial ? 

What distinction has been made between echoes ? 

* From the Greek 'Hjgwj a reflected sound, 



268 ACOUSTICS. 

be impossible to pronounce more than ten syllables in a second intel- 
ligibly, it must follow, that if the reflecting- body causing an echo 
should be so near the speaker as to return his voice in 1-10 of a se- 
cond, the last syllable only of a word uttered would be distinctly re- 
echoed, for all the preceding would be confounded together. There- 
fore, if the distance of the reflecting- object were but 56| feet, the 
sound in going and returning through twice that space would take 
up but 1-10 of a second, and the echo would consequently be mono- 
syllabic. If the distance cf the reflecting object were 113 feet two 
syllables might be returned ; and in general there would be as many 
syllables repeated as the multiples of 56£ in the number of feet 
between the source of sound and the reflector. 

112. It will be obvious that two persons may be so situated that 
one may hear the echo of the voice of the other without perceiv- 
ing the original sound ; for the voice impinging- obliquely on a re- 
flecting surface may be conveyed uninterruptedly to a person 
placed in the line of reflection, while some intervening obstacle 
may prevent the direct passage of the sound. Thus two persons 
standing one on each side of a mirror might see the reflected 
figures of each other in the glass, though an opaque body might 
entirely conceaMrom either the real figure of the other. 

113. Such echoes as have been now described would be produced 
by a single reflecting body, which would necessarily return or repeat 
but once each original sound. The most remarkable echoes, how- 
ever, are those which have been termed polyphonous, because 
they multiply sounds, or yield several repetitions of a single ori- 
ginal sound; the echo arising from successive reflections from a 
number of different surfaces. Numerous instances of extraordinary 
echoes are related by travellers and other writers. Dr. Plot, in his 
History of Oxfordshire, England, gives an account of an echo in the 
park at Woodstock, that would repeat seventeen syllables in the 
day-time, and twenty at night: the air being more elastic during 
the day than in the colder season of the night, the sound would 
travel faster, and be returned more speedily by the diurnal than 
by the nocturnal echo. On the north side of the parish church of 
Shipley, in Sussex, there is an echo which will repeat twenty-one 
syllables. 

114. Among the echoes which repeat the same sound many 
times one of the most rioted is that mentioned by Father Kircher 
and Gasper Schott in the seventeenth century, and subsequently 
by Misson and Addison, as existing at the Marquis of Simonetta's 
villa, near Milan, in Italy. It is produced by two parallel walls 
constituting the wings of the building, and the echo, which is 
best heard from a window between them, will repeat a single 

How is the number of syllables echoed necessarily limited ? 

In what cases may echoes be heard to the exclusion of direct sounds ? 

What are meant by polyphonous echoes ? 

From what do they proceed ? 

What examples of pol.vsvllabic echoes have been recorded ? 

What cases of polyphonous echoes have been noticed r 



REFLECTION OF SOUND FROM CURVED SURFACES. 269 

word more than forty times, and the report of a pistol nearly sixty 
times ; but not with perfect distinctness except early in the morn- 
ing or late in the evening-, in calm weather. There is an analo- 
gous echo at Verdun, produced by two towers distant from each 
other about 165 feet ; and a single word uttered loudly by a person 
standing between them, will be heard repeated a dozen times. 

115. On the Rhine, near Lurley, is a remarkable echo, described 
by Dr. Granville, caused by the reverberations of sound from the 
rocky banks of the river, which may be heard to the greatest ad- 
vantage from a boat in the middle of the stream. This echo repeats 
musical sounds, gradually fading on the ear till they die away ; 
and it resembles the polyphonous echoes, which are heard on the 
Lakes of Killarney, in Ireland. A wonderful echo is mentioned 
by Father Gassendi in his remarks on Diogenes Laertius, since he 
states that Boissard heard the first verse of the iEneis, 

Arma virumque cano Trojan qui primus ab oris, 

repeated eight times at the tomb of Metellus, an ancient monument 
near Rome. At Genetay, near Rouen, in Normandy, a curious 
echo is said to exist, the effect of which is such, that a person 
singing will hear only his own voice, while others at a distance 
hear the echo and not the original sound ; sometimes the reflected 
sound seems to approach, and at other times to recede, and the 
sounds are heard in different directions, according to the situation 
of the hearer. 

116. The reflection of sound, in- 
stead of producing an echo, may 
have the effect of concentrating 
sonorous vibrations so as to render 
sounds audible with the utmost 
distinctness at considerable dis- 
' B tances from the places where they 
are emitted. This may happen in consequence of repeated reflec- 
tions from a curved or polygonal surface, so that the sound being 
uttered in the focus of one reflecting surface it will be conveyed 
to the ear placed in the focus of another reflecting surface. Thus 
a sound too weak to be heard in the direct line A B, in the margi- 
nal figure, maybe augmented by reflection from B to C, and thence 
to A, and also by a number of intermediate reflections from «, 6, 
c, d, e, f, and various other points, all tending to A ; so that a 
whisper or the scratch of a pin, which could not be conveyed di- 
rectly from B to A, would be heard plainly by accumulated reflec- 
tion from different points- in the circular surface B C A. 

117. The most trifling sound may thus be heard from the oppo- 

What singularity exists in the echo of Genetay ? 

What effect, other than echoes and resonances, may be produced by 
the reflection of sound ? 
In what manner may this result be obtained ? 
Illustrate this by diagram. 

z 2 




270 ACOUSTICS. 

site side of the circular gallery at the base of the dome of St. 
Paul's cathedral, London, hence called the whispering gallery. 
There is also a whispering gallery in Gloucester cathedral, where 
a narrow passage seventy-five feet in length extends across the 
west end of the choir ; and the wall forming five sides of an octa- 
gon, the voice of a person whispering gently at one end of the 
gallery is carried by reflection to the ear of a person on the other 
side of the choir. 

118. In a very similar manner sound is concentrated by reflec- 
tion, from the focus of one reflecting surface to that of another in 
an elliptical vault. The cupola of the Baptistery of Pisa is thus 
constructed ; so that a person placed in one focus may distinctly 
hear a whisper uttered in the other focus, though it would be in- 
audible in the intermediate space. The cathedral of Girgenti, in 
Sicily, affords an example of a similar construction; in conse- 
quence of which the gentlest whisper may be plainly heard from 
the cornice behind the high altar by a person at the great western 
door, a distance of two hundred and fifty feet. The ecclesiastics, 
ignorant of this circumstance, had unluckily placed the confes- 
sional in the focus of one of the reflecting surfaces, and persons 
who happened to have found out the place whither sounds were 
conveyed, amused themselves for some time by resorting thither 
to hear secrets intended only for a confessor : at length one of 
these indiscreet listeners was punished by hearing his own wife 
confess her frailty ; and the affair becoming public, the confessional 
was removed to a more secure spot. 

119. The concentration of sounds sometimes produces very 
singular effects, of which an instance is thus related by Dr. Ar- 
nott : "It happened one day on board a ship sailing along the 
coast of Brazil, far out of sight of land, that the persons walk- 
ing on deck, when passing a particular spot, heard very distinctly 
during an hour or two, the sound of bells, varying as in human 
rejoicings. All on board came to listen, and were convinced ; 
but the phenomenon was most mysterious. Months afterwards it 
was ascertained, that at the time of observation the bells of the 
riiy of St. Salvador, on the Brazilian coast, had been ringing on 
the occasion of a festival : and their sound, therefore, favoured by 
a gentle wind, had travelled over perhaps 100 miles of smooth 
water, and had been brought to a focus by the concave sail in 
the particular situation on the deck where it was listened to."* 

120. There are some echoes for which it is more difficult to ac- 
count. Such for example, as that observed by M. Biot in the 
aqueducts of Paris, where on speaking at the extremity of a tube 
951 metres in length, the voice was repeated six times. The in- 

In what celebrated structures is the concentration of sound exemplified-' 
What is related of the cathedral of Girgenti in Sicily ? 
How have mariners occasionally experienced the effects of concen 
Ira ted sounds ? 

* Elements of Physics, vol. i. p. 5S8. 



THE INVISIBLE LADY. 271 

tervals of these echoes were equal, each being about half a second ; 
the last returning to the ear after three seconds, that is, after the 
time requisite for the sound to pass through the space of 951 me- 
tres. Similar echoes have been noticed in the long galleries of 
mines. M. Beudant observes that probably, in the experiment 
of Biot, the tubes were not laid exactly in a straight line, nor 
throughout of the same diameter ; and that in the galleries of 
mines it may be imagined that the walls or sides were not parallel.* 

121. The conveyance of articulate sounds by means of tubes 
through considerable distances from one part of a building to 
another is now commonly practised. By this method a message 
or inquiry can be communicated from a person in his study or 
office, in the upper part of a high building, to clerks or workmen 
in the lower part, without loss of time or inconvenience. 

122. The facility with which the voice thus circulates through 
tubes was probably known to the ancients, and certainly to the 
cultivators of philosophy in the middle ages. Pope Sylvester II. , 
whose proper name was Gerbert, was almost the only man of 
science living in the tenth century, and not now forgotten. By 
his contemporaries he was regarded as a magician, because among 
the wonderful machines he constructed was a speaking head of 
brass. Albertus Magnus, and Roger Bacon, in the thirteenth 
century, incurred similar odium, in consequence of their having 
formed speaking figures. There can be no doubt that each of 
these ingenious men adopted the method now described of con- 
veying sound from a distance, so that it might appear to proceed 
from an inanimate bust. 

123. By far the cleverest deception of this kind was an exhibi- 
tion which took place at Paris several years since and afterwards 
in London, appropriately styled the Invisible Lady, since the ap- 
paratus was so contrived that the voice of a female at a distance 
was heard as if it originated from a hollow globe not more than a 
foot in diameter, suspended freely from wooden framework, by 
slender ribbons. 

124. A perspective view of the machinery, and a plan of *the 
globe and adjoining parts as constructed by the inventor, M. 
Charles, are given below. It consisted of a wooden frame, much 
resembling a tent bedstead, formed by four pillars A, A, A, A, 
connected by upper cross-rails, B, B, and similar rails below, 
while it terminated above in four bent wires, C, C, proceeding 
from the angles of the frame, and meeting in a central point. The 
hollow copper ball, M, with four trumpets, T, T, issuing from it 

How may polyphonous echoes in pipes and mines be explained ? 

To what useful purpose may the conduction of sound by long tubes be 
applied ? 

What instances of ingenious deception have been formed on this mode 
of transmitting sound ? 

To what imputation did they subject their authors ? 

How was M. Charles's invisible lady constructed ? 

* Beudant Elem. do Phys., pp. 367, 368. 



272 



ACOUSTICS. 




at right angles, hung in the centre of the frame, being connected 
with the wires alone by four narrow ribbons, D, D. Any question 
or observation uttered in a low voice close to the open mouth of 
one of the trumpets elicited a reply which might be heard from 
all of them, the sound being perfectly distinct, but weak, as if it 
was emitted by a very diminutive being. 

125. The real speaker was a female concealed in an adjoining 
apartment, and the means by which her voice was made to issue 
from the globe in the manner stated were at once very simple and 
ingenious. Two of the trumpet mouths, T 1 , T 2 , as represented 
in the plan, were exactly opposite apertures leading to tubes in 
two of the cross-rails, which meeting at the angle A, opened into 
another tube descending through the pillar, and which was con- 
tinued under the floor into an adjoining apartment, where a person 
sitting might hear what was whispered into either of the trum- 
pets, and return an appropriate answer by the same channel. 
This machinery differs from the common speaking-tubes, previ- 
ously noticed, merely in the addition of the hollow ball and trum- 
petSj by means of which the voice is reflected from the cavity of 
the globe through the trumpets T 1 , T 2 , into the tube of commu- 
nication; and thus the effect produced is rendered abundantly 
mysterious to those unacquainted with the principles of Acou- 




126. The Speaking-trumpet, used by captains of ships, is an 
instrument adapted for increasing the intensity or loudness of 
sounds, by multiplied reflection. It consists of a conical tube, as 

In what manner did his machinery differ from ordinary speaking-tube6 ? 
Explain the construction of the speaking-trumpet. 



VENTRILOQUISM. 273 

represented above, open at both ends, about* three feet in length, 
and formed of copper or tin-plate. On speaking 1 slowly and dis- 
tinctly with the month applied to the opening A, the sound after 
being reflected from the sides of the tube in the direction of the 
cross-lines, will escape from the wide extremity B, and be con- 
ve) T ed to a distance proportioned to the length of the tube and the 
diameter of its bell-shaped aperture. Kircher, in his " Phonurgia 
Nova," published in 1673, claims the invention of the speaking- 
trumpet, referring to his "Musurgia," 1650, for an account of the 
instrument; but his contrivance seems to have been constructed 
on the principle of the tubes of communication mentioned above, 
rather than on that of the speaking-trumpet, which was more pro- 
bably invented by Sir Samuel Morland, who gave a description 
of it in a work which was printed in London, 1671, under the title 
of "Tuba Stentorophonica." It is by no means necessary that 
the speaking-trumpet should be composed of a metallic substance, 
for the sonorous vibrations will be propagated in the same manner 
and with equal effect through a similar tube lined with cloth. 

127. A Hearing-trumpet is nothing more than a funnel-shaped 
tube, like a reversed speaking-trumpet ; which, when the small 
end is held to the opening of the ear, conveys to the person using 
it articulate sounds from without, increased in intensity by re- 
peated reflections from the inside of the tube. M. Lecat invented 
a double acoustic tube, by which concentrated sounds might be 
conveyed to both ears at the same time ; and which may be used 
with great advantage by those whose auditory faculty is im- 
paired. 

128. The art of ventriloquism appears to depend in some de- 
gree on the reflection of sound within the mouth. Professor Du- 
gald Stewart attributed the talent of exciting the perception of 
articulate sounds, in such a manner as to give them the effect of 
emission from various distances and directions, wholly to decep- 
tion and the power of imitation. Those who have witnessed the 
curious monopolylogues, as he appropriately styles them, of Mr. 
Mathews, in his theatrical exhibitions, will readily admit that 
feigned dialogues and other vocal illusions, in which the sounds 
apparently issue from an object very near the performer, may be 
solely the effect of exquisite mimicry. 

129. The celebrated Peter Pindar, or rather Dr. Walcot, pos- 
sessed considerable talent as a mimic, and he sometimes amused 
his friends by the display of his skill. He would quit his apart- 
ment on the first floor, as if to speak to a person waiting for him, 

By whom is its invention claimed ? 

Is a metallic substance necessary to produce the effect of this instru- 
ment ? 

What improvement on the hearing-trumpet was invented by Lecat ? 

In what peculiar art is the reflection of sound applied ? 

In what manner are we to account for the deception of the ear by mi- 
mics who personate several characters at the same time ? 

What anecdote illustrates this view of the subject ? 



274 ACOUSTICS. 

and shutting the door on those within, he would stand at the stair 
head, and hold a fancied conversation with his laundress, the bard 
speaking- alternately in his own natural tone of voice, and in the 
shriller key resembling- the voice of a female. He would repre- 
sent the visiter as demanding- payment of her account, and, in 
spite of the excuses and expostulations of the bard, raising- her 
voice in reply to each apology, and becoming gradually more and 
more abusive, till at length, when the company, who heard all, 
might suppose that he had lost all patience at the woman's perti- 
nacity and insolence, the dialogue would be suddenly terminated 
by a noise which seemed to indicate that he had kicked the laun- 
dress down stairs. Such an exhibition, whimsical enough to 
those not in the secret, would obviously require much less skill 
and address than the scenes where the performer stands in pre- 
sence of the audience. 

130. The deceptions of the ventriloquist are produced in a dif- 
ferent manner, requiring not only the faculty of disguising the 
voice so as to imitate other sounds, but also the art of determining 
the apparent source of sound. Among the numberless examples 
of the feats on record relative to the professors of this art is the 
following, related as an ear-witness, by Van Dale, the author of a 
treatise on Oracles. There was, in 1685, in the hospital for the 
aged at Amsterdam, a woman, seventy-three years old, whose 
name was Barbara Jacobi, and who was visited by a vast multi- 
tude of persons on account of her talents as a ventriloquist. She 
lay on the side of a small bed, the curtains being undrawn, and 
turning as if to talk to a man near her whom she called Joachim, 
she returned answers to her own questions or remarks in a feigned 
voice. She would accuse her supposed companion of gallantries 
with other females, make replies for him, sometimes as if he was 
laughing, sometimes crying, now uttering groans, and then sing- 
ing songs, and all with such address and effect, that the illusion 
was complete ; and the by-standers occasionally would not be 
convinced that she had no associate till the}' had satisfied them- 
selves by searching the bed.* 

131. This woman, who was famous for her skill, is also men- 
tioned by Balthasar Bekker, in his curious treatise entitled "The 
Enchanted World;" and another Dutch writer, John Conrad Am- 
man, in his Dissertation on Speech, states, that he had heard her 
singular dialogues, and that the feigned voice she uttered seemed 
to issue from a spot at least two paces from her. The Abbe de la 
Chapelle, a learned Frenchman, who was a Fellow of the Royal 
Society of London, wrote a distinct work on ventriloquism,! in 

How does ventriloquism differ from mimicry ? 

What instance of their combination is recorded by Van Dale ? 

What account of the effect and its cause is given by Amman ? 

* Antonii Van Dale Polyatri Harlemensis Dissertationes de Origine 
ac Progressu Idolatrife et Superstitionum, 4to. p. 652. 

t Le Ventriloque ou l'Engastrimythe. Par M. de la Chapelle, Censeur 
Royal a Paris, &c. Deux parties. " A Londres, 1772. 12mo. 



VENTRILOQUISM. 275 

which he has collected a great number of notices of persons 
skilled in this art, and of their singular exploits. 

132. One distinguished ventriloquist to whom his work relates, 
was the Baron von Mengen, a nobleman of Vienna, who in a let- 
ter addressed to M. de la Chapelle, states, that he had acquired a 
facility in speaking as a ventriloquist, by mere practice com- 
menced when a boy, but he professes himself unable to commu- 
nicate the art to another. Amman in the passage referred to 
above, expressly asserts that the effect is produced by speaking 
during the act of inspiration, or drawing air into the lungs, in- 
stead of speaking while the air is passing out as usual. The 
Abbe de la Chapelle attempts to controvert this notion, Avhich, 
however, seems to be founded on correct observation, as articulate 
tones can be thus formed differing in intensity from those emitted 
in the customary mode. Yet some further modification of the 
speech appears to be requisite to produce all the effects described ; 
and one of the most essential peculiarities w T ill consist in the art of 
enunciating all, or nearly all, the letters of the alphabet without 
moving the lips. 

133. It is a remarkable circumstance that the art of ventrilo- 
quism is practised among the Esquimaux, by individuals who 
have acquired among their countrymen the reputation of being 
wizards. The late Captain Lyon, one of the officers who visited 
the Arctic regions a few years since, had opportunities of wit 
nessing the exhibitions of one of the most skilful of the Esqui- 
maux ventriloquists, and he published an interesting account of 
the observations he made on those occasions. One of the most 
important circumstances which he noticed was that the ventrilo- 
quist, after having uttered a protracted sound, Avhich lasted while 
Captain L. had made two inspirations after holding his breath as 
long as possible, emitted a "powerful yell, without a previous 
stop or inspiration of air."* Doubtless the previous lengthened 
sound was produced during inspiration, and therefore the succeed- 
ing yell relieved the distended lungs. This observation thus 
agrees with those which have been made on other ventriloquists. 
But there seems to be little probability that this subject will be 
perfectly understood till some skilful ventriloquist may choose to 
investigate the manner in which the vocal organs are employed in 
forming such anomalous sounds, and communicate the result of 
his researches to the public. 

Among what barbarous nations has the art of ventriloquism been prac- 
tised ? 

In what manner does Captain Lyon account for the prolonged utter- 
ance given by the Esquimaux ? 

* Private Journal of Capt. G. F. Lyon. 1824. pp. 358, 361, 366. 



276 acoustics. 



Books on the subject of Acoustics. 

Playfair's Outlines of Natural Philosophy, vol. i. pp. 281 — 291 

Robinson's Mechanical Philosophy, 8vo. vol. iv. pp. 376 — 537. 

Library of Useful Knowledge, treatise on Pneumatics, pp. 
29—31. 

Chladni Traite d'Acoustique, Paris. 

Rush's (Dr. James) Philosophy of the Human Voice, Phila. 
1827. 

Edinburgh Encyclopedia, article Acoustics. 

Cassini on Sound, Mem. of the French Academy for 1738, 
p. 128. 

Savart Recherches sur les Usages de la Membrane du Tym- 
pan. Ann. de Chim. vol. xxvi. p. 5. 

Nollet on the Hearing of Fishes, Mem. of the Fr. Acad. 1743. 

Euler on the Propagation of Pulses, Berlin Memoirs for 1765. 
p. 335. 

Dulong on the Velocity of Sound in different Gases, Ann. 
de Chim. vol. xli. p. 113. 



Works in the department of acoustics are very numerous ; but 
the number of those which treat the subject with perfect clear- 
ness, combined with that exactness which the case seems to require, 
is perhaps smaller than in most branches which have for an equal 
length of time been cultivated by the curious and the learned. 
This arises, in part, from the intrinsic difficulties of the subject; in 
part, from the fact that many persons, as stated in a preceding page, 
are insensible to the nicer shades and distinctions of sound, and 
in no small degree from the discouragements long felt in attempts 
to make the deductions of theoretical investigation correspond with 
experimental results. The far-reaching mind of Newton himself, 
was not able to grasp all the causes which modify the transmis- 
sion of sound. Indeed the law, of La Place, that the theoretical 
result of Newton must be corrected by multiplying it into the 
square root of the ratio of the specific heat of air under a constant 
pressure, to its specific heat under a constant volume, could not pos- 
sibly have been applied in Newton's time ; for the whole doctrine 
of specific heats was then unknown. Again, the means of ex- 
hibiting, in all their variety, the numerous phenomena of vibration, 
have only for the last few years been supplied by the labours of 
Chladni, Savart, Biot, Colladon, Faraday and others. The art of 
composition in music, and skill in its performance, have sometimes 
been mistaken for the science from which they derive their princi- 
ples. The art of rhetoric has in like manner been conceived to 
constitute the science of vocal utterance, until Dr. Push pushed 
his analytical researches to the extent of dissecting ,ie very ele- 
ments of speech, and displaying those operations of the organs 
which combine to produce or to modify every element.— -Ed. 



PYRONOMICS. 

1. Among those branches of natural philosophy which have at- 
tained the rank and importance of distinct sciences, in conse- 
quence of the researches of our contemporaries, must be included 
that, the object of which is, to explore the properties and opera- 
tions of heat. To designate this department of human knowledge, 
Leslie has adopted the term Pyronomics, which signifies the laws 
of heat.* The effects of heat, or rather of relative temperature, 
have so striking an influence on all bodies around us, and it pro- 
duces such varied and singular consequences, that whether con- 
sidered as arising from the modifications of matter with which we 
are most intimately acquainted, or as depending on the presence 
of some* peculiar subtile agent, it must be desirable that they 
should be classed and arranged so as to form a systematic series 
of facts and observations ; and to such a system the appellation 
Pyronomics may be appropriated, as expressive of the objects to 
which it relates. 

2. The cause of heat has formed a subject of controversy among 
modern philosophers ; some of them ascribing the phenomena in 
which it is concerned to intestine motions of the minute particles of 
bodies, analagous to those which give rise to sound ; while others 
have endeavoured to prove that heat arises from the presence 
of a peculiar fluid, or ethereal kind of matter, such as that which 
has been regarded as the cause of light. If such a fluid exists, it 
must be destitute of weight, for it has been ascertained from ex- 
periment that the addition of heat to any substance produces no 
alteration whatever in its gravitative force. 

3. Dr. George Fordyce instituted researches concerning the 
effect of temperature on the weight of bodies, Avhence it was con- 
cluded that the abstraction of heat from water occasioned an in- 
crease of weight. He inclosed 1700 grains of water in a glass 
globe, and having sealed it hermetically, after ascertaining the 
weight of the globe and its contents with the utmost accuracy, he 
immersed it in a freezing mixture, and on weighing it again after 
the liquid had become entirely congealed, he found it had gained 
3-1.6 of a grain. j~ Guyton de Morveau, and Chaussier, made cor- 
responding experiments in France, on water and sulpu iric acid, 
from the results of which they drew the same inferences. 

To what is the term Pyronomics properly applied ? 

To what cause have different philosophers attributed the phenomena 
of heat ? 

To what result were Fordyce, Morveau, and Chaussier conducted ia 
regard to the effect of temperature on the weight of bodies ? 



* From the Greek nop, fire, and No^oc, a law. 
t See Philosophical Transactions vol.lxw. 

2 A 2:7 



278 PYRONOMICS. 

4. Other philosophers, however, made comparative trials of the 
weight of water and sulphuric acid in the liquid state, and when 
reduced by cooling to the solid form, without being able to detect 
any difference of weight appreciable by the most delicate balances. 
The apparent effect of the variation of temperature on the weight 
of bodies as noticed in the above experiments, may be attributed 
to the influence of the frozen mass on the density of the surround- 
ing air ; therefore, if we admit the observations to be perfectly 
correct, it may still be contended that they are not conclusive. 

5. Count Rumford, having suspended a bottle containing wa- 
ter, and another containing spirits of wine, to the arms of a balance, 
and adjusted them so as to be exactly in equilibrium, he found 
that it remained undisturbed when the water was completely fro- 
zen, though the heat the water had lost must have been more than 
sufficient to have made an equal weight of gold red-hot. If, there- 
fore, with Lavoisier and his associates, (the founders of what has 
been styled the Antiphlogistic System of Chemistry,) we suppose 
heat to be matter rather than motion, it must be allowed to be an 
imponderable fluid, and also, as denominated by some philoso- 
phers, an incoercible fluid, for though it passes through some bo- 
dies with more difficulty than through others, there is no body or 
or kind of matter which can completely arrest its progress. 

6. The terms Caloric* and Matter of Heat have been adopted 
to designate the hypothetical causes of those phenomena which 
are referred to the science of Pyronomics ; and without admitting 
the separate existence of such an agent as the caloric of the French 
chemists, the term may sometimes be advantageously employed 
to denote the amount of effect produced by relative changes of 
temperature in the same or in different bodies. 

7. Various phrases occur in our own and in ether languages 
expressive of the effects resulting from alterations of temperature, 
both as regards the impression on our senses, and the changes of 
form or structure produced in the bodies around us. When we 
touch a substance more heated than the hand applied to it, the 
sensation arising from it is styled warmth ; and that caused by a 
substance less heated is named chilliness or cold. But warmth 
and chilliness, or heat and cold, thus used, are merely relative 
terms ; for a substance which would excite in one person the sen- 
sation of heat might at the same time seem cold to another ; and 
if a man, after holding one hand near a fire for a few minutes, and 

Flow has the weight of bodies, as affected by heat, been explained ? 

In what manner did Rumford seek to determine the question of the 
ponderability of heat ? 

What other distinguishing property, besides that of imponderable, be- 
longs to the nature of heat? 

To what is the term caloric applied ? 

How may it be shown that hot and cold, warmth and chilliness, are re- 
lative terms ? 

* From the Latin color, heat. 



EFFECTS OF CHANGE OF TEMPERATURE. 279 

laying the other on a cold stone or marble slab, were to dip both 
in a basin of lukewarm water, the liquid would warm the cold 
hand and cool the warm one. 

8. " There is, perhaps, no subject," says Hutton, " in which the 
language and ideas of men are more vague, or more distant from 
true science, than in those of heat and cold. The reason of this 
will not be difficult to assign. Heat is a term which is applied 
in different cases ; for it is both a principle of action in external 
things, and a principle of passion in our sensitive mind. But 
this is only a part of that intricacy with which this apparent- 
ly simple subject is necessarily involved ; for when heat is a 
principle of action in external things, there are two different effects 
which occasionally follow this principle as a cause. First, bodies 
are by heat distended or expanded in their volume : here is one 
distinct effect. Secondly, without being thus distended by heat, 
bodies, in receiving that distending cause, are made to lose their 
hardness, or concretion, and become fluid in their substance : here, 
then, is an effect distinctly different from the other ; and both of 
these are perfectly different from the feeling of heat and cold 
which is the immediate information of the sense."* 

9. Among the terms indicating various effects or operations of 
heat, or the appearances which we are accustomed to ascribe to 
its action on the several substances around us, are some which 
imply a connexion between heat and light : thus a body like red- 
hot iron, or burning coals, is said to glow or be glowing; a lumi- 
nous vapour issuing from a burning body is called flame, and 
such a body may be said to flame or blaze ; when any substance 
exhibiting these appearances becomes dissipated or dispersed 
through the air, either wholly or partially, the operation is styled 
burning or combustion ; and when a heated body emits light with- 
out combustion, it is said to be incandescent, or in a state of incan- 
desence. The appearance of heat and light in conjunction is often 
designated fire, a term used by ancient philosophers as character- 
istic of the matter of heat, and regarded as one of the four ele- 
ments. 

10. The effects of heat on our senses are too variable and falla- 
cious to afford any important assistance in the investigation of its 
nature and properties ; and the principles which form the founda- 
tion of the science of Pyronomics must therefore be derived from 
the consideration of those phenomena which always appear under 
certain circumstances, so that we can produce them at pleasure 



Whence has arisen the vagueness of language employed on this sub- 
ject P 

What two circumstances have particularly contributed to increase the 
misconception of terms in relation to it p 

What is meant by glo-wing ? burning and incandescence ? 

What character was by the ancient philosophers attributed to fire ? 

On what must we rely for obtaining the principles of pyronomics ? 

* A Dissertation on the Philosophy of Light, Heat, and Fire, by J. 
Hutton. 



280 FYROXOMICS. 

by proper arrangements, and estimate with precision the results 
of combinations by means of which heat is accumulated or dis- 
persed', and its operation on bodies induced, modified, or termi- 
nated. 

11. The distinguishing properties or effects of heat, or those 
phenomena which arise from its addition to material bodies, or 
more simply from the augmentation of their temperature, are of 
three kinds. 1. Mere dilatation, or increase of volume, which 
occurs in solids, liquids, or gases, without any change of form. 
2. Transformation of a solid to the liquid state, as in dissolving 
ice or melting lead ; and of a liquid to the gaseous state, as in 
forming steam from water, or vapour from any liquid, by boiling 
or distillation. 3. Destruction of the texture of bodies by com- 
bustion, in consequence of which new combinations of the con- 
stituent particles of bodies are formed, the investigation of which 
falls within the province of the chemist rather than of the natural 
philosopher. 



Sources of Heat. 

12. Before proceeding to notice in detail the properties and phe- 
nomena of heat, some attention may be advantageously directed to 
the sources or efficient causes of heat. These are radiation from 
the sun together with light; certain mechanical operations, as 
friction, percussion, and compression ; and a variety of chemical 
operations, especially combustion. Heat is also evolved from 
living animals and vegetables, either by the immediate influence 
of the vital powers of organized nature, or in consequence of 
chemical processes, modified by the peculiar properties of organic 
matter. 

13. That the sun is the grand fountain of heat, or the prin- 
cipal cause of elevation of temperature by its action on bodies 
exposed to its rays, is a fact too obvious to require demonstration. 
As to the manner in which the effect is produced, different opin- 
ions have been entertained. The generally received popular notion 
concerning the nature and constitution of the sun, as the source 
of light and heat, is that of an inextinguishable mass of matter 
in a state of intense conflagration ; or, in other words, a globe of 
perpetual fire, the idea of which has manifestly been derived from 
comparison of the property of giving heat and light common to 
the sun, and to flames arising from combustible substances. 

14. Sir "William Herschel entertained a very different opinion 
relative to the nature of the solar orb, which from numerous te- 
lescopic observations, he was led to imagine to be an opaque 

Of how many kinds are the phenomena arising from the augmentation 
of temperature ? 

How many and what are the known sources of heat ? 

Whence has the idea of the igneous nature of the sun been derived ? 

"What view did Sir W. Herschel entertain on this subject 1 



HEAT OF THE SUN. 281 

globular mass, encompassed by an atmosphere consisting of trans- 
parent elastic fluids, from the decomposition of which heat and 
light were continually proceeding; and he conceived that the body 
of the sun, far from being the seat or fountain of perpetual fire, 
might with probability be regarded as a world furnished and in- 
habited like the earth to which we are confined. Interesting, 
however, as such speculations may be, they are not necessarily 
connected with the subject before us, and must therefore be dis- 
missed with this short notice. 

15. In reference to the sun as a principal source of heat, the 
question will recur, whether heat is a peculiar kind of ethereal 
matter, which may be emitted from the sun, or rather according 
to Herschel's hypothesis from the solar atmosphere, and radiating 
through space together with light, be absorbed by various bodies 
on the surfaces of the earth and other planets, producing the ef- 
fects of sensible warmth, expansion of solids and fluids, melting 
of solids, and boiling or evaporation of liquids, and in some cases, 
destruction of substance accompanying chemical combinations ; — 
or whether heat and its concomitant phenomena just mentioned 
may not arise from the propagation of motion through space ; the 
sun or its atmosphere being the grand exciting cause of heat, and 
producing it in a manner analogous to that in which sound is pro- 
duced by a bell. 

16. According to the former mode of theorizing we must admit 
the existence of a peculiar penetrating fluid emanating from the 
region of the sun, and entering with greater or less facility into 
all terrestrial bodies, on which it produces its characteristic ef- 
fects : and on the latter supposition, it must be admitted that 
there exists in the space between the sun and the planets an ethe- 
real medium of inconceivable tenuity, through which vibrations 
can be propagated with velocity immensely beyond those to which 
are to be attributed the phenomena of sound. 

17. Heat, as depending on the influence of the sun, is unequally 
distributed over the surface of the earth. Owing to the oblique 
position of the earth's axis, the solar rays fall more directly on 
certain parts of its surface at one season of the year than at ano- 
ther ; and the inequality of effect arising from this cause, is in 
some degree compensated by the greater length of time during 
which the sun shines continuously on those parts of the earth 
where the direction of the solar rays is least favourable. Thus 
under the equator the length of the days never exceeds twelve 
hours, while they increase in extent on proceeding towards the 
poles, and within the arctic and antarctic circles, the sun shines 
six months together, and then for six months remains invisible. 

What part is acted by the sun on the supposition that heat is mate- 
rial ? 

What on that of its being the vibration of an ethereal fluid ? 

In what manner is the heat of the sun distributed over the earth ? 

How does the obliquity of the sun's annual path to the plane of the 
equator affect the heat of different parts of the globe ? 



282 PYRONOMICS. 

/ 18. The relative influence of the sun as the cause of heat, at 
different parts of the earth's surface, attracted the attention of 
Dr. Halley, who laid the result of his observations before the Royal 
Society, in a " Discourse concerning the Proportional Heat of the 
Sun in all Latitudes, with the method of collecting the same." 
He notices the influence of local circumstances on the temperature 
of different regions, referring to the effect of the neighbourhood of 
high mountains, and wide sandy deserts. But his grand object 
was to ascertain the relation between temperature and latitude, as 
depending on the direction of the sun's rays, and the respective 
intervals during which they operate. 

19. Since the beginning of the present century, a vast number 
of facts have been accumulated relative to this interesting subject; 
and the observations on temperature made in different parts of the 
world, and especially in high northern latitudes, have enabled 
men of science to form much more accurate conclusions relative 
to the temperature of the earth as influenced by its position at dif- 
ferent seasons of the year, than those deduced from mere theoreti- 
cal calculations. 

20. From a comparison of the researches of Humboldt in the 
equatorial regions of the earth, with those of Captains Scoresby 
and Parry in the colder climates of the north, it has been con- 
cluded that there must exist two poles of maximum cold, one in 
America, and the other in Asia ; and that the utmost depression 
of temperature takes place, not at the north and south poles of the 
earth, but at those imaginary points. Temperature and climate 
must chiefly depend on the figure of the great continents of the 
world ; besides which there are a variety of circumstances which 
must tend to modify the influence of solar heat as connected with 
the situation of places on the surface of the earth. 

21. Mr. Atkinson, in a paper in the " Memoirs of the Astronomi- 
cal Society of London," (vol. ii.) estimates the mean temperature of 
the equator at 86°.55 ; and that of the pole at — 10°. 53. Mr. Forbes 
regards the former as decidedly too great, and says " it is proba- 
ble that the mean temperature of the equator does not exceed 81°. 5 
or 82°." The mean temperature at the pole can only be inferred 
from observations at very high latitudes ; and hence the following 
table of mean temperature becomes interesting and important. 

Lat. Mean Temp. Observer. 

Melville Island - - - 74£° - 1^° - - - Parry. 

Port Bowen - - - - 73£ -■--_{! 4 --- The same. 

What point did Halley seek to determine in regard to solar heat ? 

Is the temperature of different parts of the earth's surface dependent 
solely on latitude ? 

What important conclusion has been deduced from the researches of 
travellers in the polar and equatorial regions ? 

What is Mr. Forbes's estimate of the mean temperature of the equa 
tor? 

How can we infer that of the pole ? 

What is the mean temperature of the year at Melville Island ? 

What is its distance in degrees from the north pole ? 



CENTRAL HEAT OF THE EARTH. 283 

Lnt. Mean Temp. Observer. 

rgloolik 69| - - - + 7 - - - Parry. 

Winter Island - - - 66$ - - -f <H - - - The same. 

Fort Enterprise - - - 64£ - - - -f 15^ - - - Franklin. 

22. " M. Arago had concluded from the results of Scoresby, 
Parry, and Franklin, that the mean temperature of the pole is 13° 
Fah. This, however, is upon the idea that the cold is at a maxi- 
mum at the pole, which is not probable : it cannot, however, be 
much short of that intense decree."* 

23. The relative decrease of heat in ascending 1 above the sur- 
face of the earth is a subject highly deserving - of investigation. 
Mr. Forbes says, "The true law of decrease of temperature, such 
as it would be if the earth was removed, must be sought for proba- 
bly by successive stages of balloon observation, commencing - at a 
considerable heig-ht above the surface." The best observations 
on the relative diminution of heat at increasing - heights, are those 
of Humboldt, derived from experiments made in the equatorial re- 
gions of America. The g-eneral result of his researches gives 121 
toises of ascent for a diminution of 1 deg. of Reaumur's thermo- 
meter. Comparative observations at Geneva and on Mount St. 
Bernard afford a coincident result highly remarkable, the difference 
of mean temperature of the two stations being 8 deg. 64 min., 
Reaumur, for 1069 toises, which gives 123^ for 1 deg. Reaumur, 
or 352 feet for 1 deg. Fahrenheit , and this is probably' the most 
correct mean result which can at present be attained. j~ 

2-1. An inquiry has been started whether the climate of a par- 
ticular place, or that of the globe in general, has materially altered 
during the period of historic record ; and some writers have been 
inclined to decide in the affirmative, alleging the statements of 
historians that the vine was cultivated extensively for the pro- 
duction of wine in England formerly, though the summers in 
that country are now too cold to bring the fruit to the requisite 
degree of maturity. Circumstances of this nature, however, can- 
not be considered as decisive ; and it may be generally con- 
cluded that we have no authority for assuming such a change. 

25. Yet though the temperature of the earth may be regarded 
as permanent, so far as it depends on the heat derived from the 
sun, there seems to be great reason for believing that the whole 

What is Arago's conclusion respecting polar mean temperature ? 

How is the decrease of temperature above (be earth's surface to be 
known ? 

What appears to be about the mean rate of diminution in temperature, 
according- to increase in height ? 

From what observations has this result been obtained ? 

What may we infer respecting the present compared with former states, 
of terrestrial climates ? 

* Report upon the Recent Progress and Present State of Meteorology. 
Bv James D. Forbes, F. R. S., in Rep. of the British Association for 
1832, p. 216. 

t Idem, p. 219. 



284 PYRONOMICS. 

mass of the terrestrial globe is undergoing a gradual process of 
cooling, from an originally very intense temperature. Baron 
Fourier, who has distinguished himself by his investigations re- 
lating to this curious topic, has proved that the heat may be very 
intense at a short distance from the surface, and ) r et from the ex- 
tremely bad conducting power of the crust or exterior strata of the 
earth, that it may exert no sensible influence on the climate : he 
actually computes it as not amounting to 1-30 of a degree of the 
centigrade thermometer. Towards the centre of the earth the 
beat may be of the most extreme intensity, and the phenomena of 
earthquakes and volcanoes may be imputed to its influence. 

26. The process of cooling, which at first must have been com- 
paratively rapid, may be considered as having reached such a rate 
as to be imperceptible. From experiments made at Paris, in the 
caves under the Observatory, it is probable that the influence of 
the solar rays does not extend more than about 100 feet beneath 
the surface. Therefore the heat there will be nearly invariable ; 
and throughout the superior strata a constant influx and efflux of 
heat must be going on. As the influence of the sun does not ex- 
tend beyond a certain depth beneath the surface of the earth, it 
might be expected that beyond such depth the temperature would 
continue the same all the year round in every inferior stratum re- 
latively to its position; and that this is the case has been ascer- 
tained by M. Cordier, from a collation of numerous facts observed 
in Cornwall, Saxony, Brittany, Switzerland, America, and other 
parts of the world. It also appears that in all the inferior strata 
the temperature increases as we descend, without any exception : 
a circumstance decisively proving, that there must be a source of 
heat in the centre of the earth.* 

27. Hence^ it may be concluded, in conformity with the most 
rational geological speculations, that the planet which we inhabit 
was at a very remote period in the state of fusion, and like other 
semi-fluid masses revolving rapidly under the influence of central 
forces, it has assumed its peculiar form, a flattened spheroid. 
During how many ages the terrestrial globe continued to emit heat 
from its surface before compact strata were formed, such as the 
various modifications of primitive rocks which we behold, and 
how much longer time elapsed before those rocks became the 

On what other cause than solar heat does climate depend ? 

What conclusions has Fourier derived from his investigations of this 
suhject ? 

To what cause may earthquakes and volcanoes be imputed ? 

To wfiat depth beneath the surface of the ground does the influence of 
solar heat probably extend ? 

What is constantly taking place at levels above the invariable stratum? 

How is the temperature of the strata, below the invariable one, found 
to be at different seasons ? 
/ What relation has it to the depth of die several lower beds? 

What does this prove in regard to the temperature of the central parts 
of the earth ? 

* Report of British Association, p. 221. 



PRODUCTION OF HEAT BY FRICTION. 285 

basis of this world of land and wateaf, numerously peopled with 
living beings as at present, it would be utterly useless to attempt 
to conjecture. It is sufficient for us to be able to state, as the re- 
sult of the most accurate and extensive observations, that the in- 
ternal heat of the earth no longer affects in a sensible degree the 
temperature of its surface, or of the strata immediately beneath 
the surface ; and therefore the varieties of climate, and the alter- 
nations of heat and cold in the different seasons of the year, as 
well as the changes attributable to incidental causes, are chiefly 
owing to the influence of the sun, as the general efficient source 
of heat.* 

28. Among the mechanical means of producing, or rather of 
exciting heat, friction is perhaps the most usual and effective. In 
sawing wood, or boring metal, it may be observed that the sub- 
stances thus exposed to friction soon become sensibly warm. 
The wheels of carriages sometimes take fire, from friction against 
the axles when in rapid motion. In some rude countries, as in 
Patagonia, the inhabitants avail themselves of this mode of pro- 
curing fire. They either rub together two pieces of hard dry 
wood till flame arises, or more artificially insert the blunt-pointed 
extremity of a rod of hard wood in a small cavity in a thick plank, 

What bearing have the observed facts in regard to subterranean heat 
upon geological theories ? 

What effect has the internal heat of the earth on the temperature of 
its surface ? 

By what mechanical means may heat be excited ? 

What remarkable facts prove the efficacy of friction in producing 
heat ? 

* Some very remarkable instances have been recorded of extreme 
heat, as noticed by several observers. In Winkler's Elements of Natu- 
ral Philosophy, vol. i. pp. 179 — 182, are two tables of very high and very 
low temperatures observed at different times, and in various situations, 
collected by Professor Heinsius. The highest atmospheric temperature 
which he records was observed at Senegal, on the coast of Africa, in lat. 
16° N. when the heat was 86^° of Delisle's thermometer, corresponding 
to 108^° Fahrenheit. This temperature was considerably below that ob- 
served at Bagdad, in August, 1819, as stated in the Journal of Science, 
Literature, and the Arts, edited at the Royal Institution, 1820, vol. ix. 
p. 423. "On the 26th of August, last year (1819), the thermometer at 
Bagdad rose in the shade to 120° Fahrenheit, and at midnight was 108°: 
many persons died, and the priests propagated a report that the day of 
judgment was at hand." The greatest heat accurately observed in Eng- 
land, of which we have authentic accounts, took place in 1808 and 1825 ; 
July 13, 1808, the thermometer, according to the Royal Society's Regis- 
ter, rose to 93°.5 ; and Mr. H. Cavendish's thermometer at Clapham, to 
96°. Dr. Heberden observed the heat in July, 1825, and found that on the 
18th of that month the thermometer stood at 96°, and on the following 
dav at 95°.— See Philos. Trans. 1826, part ii. p. 69. 

In different parts of the United States the thermometer is frequently 
known to rise, for a few hours at a time, to 95 or 100 degrees. On the 
8th and 9th, 26th and 27th of July, 1834, the thermometer in Philadel- 
phia stood at from 94 to 98 degrees, according to different exposures. — 
Ed. 



280 PYRONOMICS. 

and turning- it with great velocity between their hands thus obtain 
sparks and flame. 

29. Count Rumford instituted some important experiments on 
the effect of friction in producing heat.* Having- observed that 
great heat was excited during the operation of boring cannon, hfl 
procured an unbored cannon, with the large projecting piece two 
feet beyond its surface, which is usually cast with the cannon to 
ensure its solidity; this projecting piece was boared and reduced 
to the form of a hollow cylinder, attached to the cannon by a 
small neck; the apparatus being wrapped in flannel to prevent 
the escape of heat, it w T as made to revolve on its axes by the 
power of horses, while a steel borer pressed against the bottom 
of the cylinder. The temperature of the metal at the commence- 
ment of the operation was 60 deg. and the cylinder, having made 
960 revolutions in half an hour, it was stopped, and the tempera- 
ture was found raised to 130 deg. In another experiment a borer 
was made to revolve in a cylinder of brass, partly bored, thirty- 
two times in a minute ; the cylinder was inclosed in a box contain- 
ing 18 pounds of water, the temperature of which was at first 60 
deg., but rose in an hour to 107, and in two hours and a half the 
water boiled. 

Stockenschneider, an ingenious mechanic of Nieuburg on the 
Weser, invented a machine, by means of wmich great heat might 
be produced, and water boiled by friction. 

30. Air does not appear to be necessary to the production of 
heat by the attrition of solid bodies. Boyle procured sensible 
heat by making two pieces of brass move rapidly in contact under 
an exhausted receiver. Pictet, of Geneva, repeated the experi- 
ment with success, and found that the introduction of a soft sub- 
stance between the rubbing surfaces, such as cotton, occasioned 
an increase of heat. Sir H. Davy insulated an apparatus for ex- 
citing heat by friction, by placing it on ice, in the vacuum of an 
air-pump, under wmich circumstances heat was produced. He 
likewise ascertained that two pieces of ice might be melted by 
rubbing against each other, either in the air of a room below the 
freezing point, or under an exhausted receiver. 

What practice among rude nations is founded on this principle ? 
In what manner did Rumford investigate the relation of heat to friction? 
To what result do his experiments conduct us? 
What applications have been made of this principle ? 
What extraoadinary results were obtained by Davy in his experiments 
on friction ? 

* The experiments of Rumford seem to prove the incorrectness of that 
theory which ascribes a material character to caloric ; and as he ascer- 
tained that the borings taken from his cannon had not undergone any di- 
minution of capacity for heat, it is difficult to ascribe the vast amount of 
heat developed to any other cause than the vibration of the metal pro- 
duced by the mechanical operations of rubbing and abrading. — Ed. 

+ A plan has been started in New England of heating manufactories 
and other buildings by the friction of metallic wheels, actuated by the 
same moving power which drives the machinery. — En. 



COMBUSTION. 287 

31 . Compression produces heat either in solids, liquids, or gases. 
An iron bar may be hammered till it is red hot; and water strongly 
compressed gives out heat, as appears from the experiments of 
Dessaignes, as well as from the interesting researches of Mr. 
Perkins on the compressibility of liquids, which have been noticed 
elsewhere.* Solids also give out heat when violently extended, 
as may be ascertained by stretching quickly a piece of Indian 
rubber, and immediately applying it to the lip, when a sensible 
degree of warmth will be felt. Mr. Barlow, in his acoount of 
some experiments on the cohesion of malleable iron, states it as a 
curious fact, and deserving the attention of philosophers, that fre- 
quently at the moment of rupture the bar acquired such a degree 
of heat in the fractured part as scarcely to suffer a person to hold 
the bar grasped in his hand, without a slight painful sensation of 
burning. | 

32. But the effect of compression is exhibited in a more striking 
manner in the production of heat from gaseous fluids, as common 
air. When air is forcibly compressed by driving down the piston 
of a syringe, nearly closed at the end, great heat is produced: 
and syringes have been construCed for the express purpose of 
procuring fire, the heat evolved by the compression of air in this 
manner being sufficient to kindle dry tinder or touchpaper. 

33. The chemical operations in the progress of which heat is 
produced are numerous, and among the most remarkable causes 
of the evolution of heat from bodies becoming united, so as to 
form chemical compounds, are those arising from combustion. All 
substances are not capable of undergoing combustion, and hence 
the division of bodies into two classes, namely, combustibles, or 
inflammable bodies, and incombustibles, or non-inflammable bo- 
dies. Among the former are vegetable substances in general, as 
wood, charcoal, and oils; most animal substances, as hair, wool, 
horn, and fat; and all metallic bodies. 

34. The class of non-combustibles includes stones, glass, and 
salts. The latter, when exposed to high degrees of heat, under 
such circumstances that they cannot undergo chemical decompo- 
sition, may be made to display the usual appearance of fire, or the 
combination of light and heat, variously designated by the terms 
glowing, red heat, or white heat, denoting different degrees of 
incandescence, and when no alteration has been produced by the 
high temperature to which they may have been exposed. But 
combustible bodies are very differently affected by heat. Some 

What calorific action attends mechanical compression } 

Which class of natural hodies illustrates most strikingly the influence 
of condensation ? 

What division of hodies has been formed in reference to the property 
of undergoing combustion ? 

What natural substances belong to each of these classes ? 

Describe the effects of heat on these different classes. 

* See Treatise on Hydrostatics, Nos. 13 — 15. 

+ Encyclopxd. Metropol. — .Mixed Sciences, p. 70. 



288 PYROXOM1CS. 

of them at comparatively low temperatures become combined with 
the oxygen gas contained in the atmosphere around them, and 
they all undergo similar transformations at certain temperatures, 
and during such processes heat in the form of fire is frequently 
exhibited. 

35. Among the simple instances of the effect of chemical com- 
bination in causing the appearance of heat may be noticed the 
increase of temperature that takes place when water is mixed 
with alcohol, and which may be readily perceived on applying the 
hand to a phial containing the two fluids just after they have been 
introduced into it. But the mixture of water with sulphuric acid, 
or, as it is commonly called, oil of vitriol, causes a much greater 
augmentation of temperature than the preceding; for if an ounce 
of sulphuric acid be poured into a bottle, containing eight ounces 
of water, the glass will be so much heated as to render it impossi- 
ble to hold it ; and a more violent heat may be produced by increas- 
ing the proportion of the acid. 

Characteristic Effects or Properties of Heat. 

I. DILITATION OR EXPANSION OF BODIES. 

36. The most obvious and direct effect of heat or exaltation of 
temperature is to add to the bulk of the heated body, or to increase 
its dimensions, generally in all directions. This takes place in 
solids, liquids, and gases, without altering their essential proper- 
ties. The expansive effect of heat on solids, 
may be exhibited by means of a cylindrical 
bar of iron, as represented in the marginal 
figure. When cold, it will be found that the 
cylinder A B will exactly fit into the space 
C, in the brass gauge annexed ; and it will 
also pass through the aperture D ; but when 
heated by plunging it for some time into boil- 
ing water, it will be so much expanded that 
it will no longer fit into the space, or enter 

the aperture. If the bar be cooled,. either slowly by exposure to 
the air, or suddenly by covering it with ice or snow, it will again 
be contracted, and pass into the cavities as before. The more 
highly the bar is heated the greater will be the amount of its ex- 
pansion ; and on the contrary, when cooled, its contraction will be 
in proportion to the reduction of its temperature. 

37. The effect of heat in expanding solid bodies, and especially 
metals, has been advantageously applied to practical purposes. 

What examples illustrate the effect of chemical combination on the (le- 
vel opement of heat ? 

What immediate alteration follows the increase of temperature in ali 
forms of matter ? 

In what manner may it be easily exhibited in the case of solid matter ? 

What useful applications are made of expansion in the common arts 
of life ? 




DILATATION OF SOLIDS BY HEAT. 289 

Thus coopers, in fixing iron hoops on a cask, make them previously 
very hot, and being adapted in that state to the periphery of the 
cask, their contraction in cooling binds together the staves of the 
cask. Wheelwrights also nail on the iron tire or band, while it is 
nearly red hot, to the wooden wheel of a carriage, and as the meta! 
contracts in cooling, it clasps the parts firmly together. 

38. The expansibility and contractibility of iron as an effect of 
temperature demands the particular attention of architects and en- 
gineers, now that metal is so frequently substituted for wood and 
stone in the construction of roofs of buildings, pillars, arches, and 
for other purposes. Due allowance should always be made for 
any alteration of dimensions in metallic beams or supporters, de- 
pending on alternations of heat and cold at different seasons of 
the year, or arising from other causes. In the iron arches of South- 
wark Bridge, erected by the late Mr. John Rennie, over the Thames, 
the extreme variations of atmospheric temperature, occasion a dif- 
ference of height at different times, amounting to about one inch. 

39. A curious example of the influence of heat on the dimen- 
sions of solids was exhibited some years since at Paris, in the 
method adopted for restoring to a perpendicular direction the de- 
clining walls of a gallery in the Abbey of St. Martin, now the Con- 
servatory of Arts and Trades. The weight of the roof had pres- 
sed outwards the side walls of the structure, and excited appre- 
hensions for its safety, when M. Molard contrived to render it 
secure by the following process : Several holes were made in the 
walls opposite to each other, through which were introduced iron 
bars stretching across the gallery, with their extremities extending 
beyond the walls; and to these projecting parts were screwed 
strong iron plates, or rather large broad nuts. Each alternate bar 
was then heated by means of powerful lamps, and their lengths 
being thus increased, the nuts which had become advanced beyond 
the walls were screwed up close to it, and the bars suffered to 
cool. The powerful contraction of the bars drew closer the walls 
of the building ; and the same process being applied to the inter- 
mediate bars, and repeated several times, the walls were gradually 
and steadily restored to the upright position, and the danger appre- 
hended from their declension was averted. 

40. Musschenbroek ascertained that heat not only expands me- 
tals, but also different kinds of stones, chalk, burnt brick, and 
glass. Such substances, however, must be perfectly freed from 
moisture, otherwise increase of temperature will occasion contrac- 
tion of volume, by dissipating the moisture. Thus wood some- 
times acquires an increase of specific gravity by drying. From 

To what classes of artisans is this branch of the subject particularly- 
important? Why ? 

What exemplification of this is seen in bridge building; ? 

Describe the method of Molard to restore walls to their vertical posi- 
tion. 

In what case may an apparent contraction follow the application o r 
heat? 

SB 



290 PYROXOMICS. 

some experiments to determine the weight of different kinds of 
wood at various degrees of dryness, recorded by Mr. Barlow, it 
appears, that in some cases there is a considerable augmentation 
of specific gravity. A piece of Riga fir, 1 1 inches thick, lost \ of 
an inch in seasoning, and the weight of a cubic foot was increased 
from 546 ounces to 562 ; a piece of American pitch pine, 7? inches 
in thickness lost f of an inch, and the increase of weight of a cubic 
foot was as 518 to 524 ; a block of Halifax spruce spar, 5^ inches in 
diameter, was reduced to 5f , and the difference of specific gravity 
was as 541 to 544 ; and a block of Canada spruce spar, 4 3 inches 
in diameter, lostf of an inch, and the difference of specific gravity, 
or weight of a cubic foot, was in the ratio of 485 to 512 ; but in 
most other cases, the loss of weight was greater in proportion than 
the diminution of bulk, so that the specific gravity was dimi- 
nished.* 

41. The effect of temperature in the expansion and contraction 
of glass is an object of common observation, and becomes the 
cause of frequent accidents. Though the degree of expansion 
which takes place in glass at any given temperature is proportion- 
ally much less considerable than that produced in metals, platina 
excepted, yet from the irregularity of the effect, glass is easily 
broken by the sudden application of heat. Glass goblets and 
tumblers are very liable to fracture, when water heated almost to 
the boiling point is poured into them ; and the danger will increase 
in proportion to the thickness of the glass ; for this substance, ad- 
mitting heat to pass through it but slowly, the inner surface be- 
comes heated and distended by the hot water before the outer sur- 
face, and the irregular expansion causes the vessel to break. Jn 
this manner, the glass chimneys now in general use for oil-lamps 
and gas-burners are often destro3 r ed. M. Cadet de Vaux states 
that the danger of fracture may be prevented by making a minute 
notch in the bottom of the tube with a diamond; and in an esta- 
blishment where six lamps were lighted every day, this precaution 
being adopted, not a single glass was broken by heat in the course 
of nine years. A bottle of wine placed near the fire in cold weather, 
will sometimes fly, as it is termed, especially if a draught of air 
falls on one side while the other is receiving heat; and the glass 
cylinder or plate of an electrical machine may be cracked and 
spoiled by incautiously placing it in a similar situation. 

42. On the relative expansibility of different metals by heat de- 
pends the operation of compensating pendulums, used for time- 
keepers and astronomical clocks. f 

Is the increase of density a uniform result of the process of drying 
wood ? 

State the experiments on this subject. 

What peculiar quality in glass renders the effect of expansion in that 
substance conspicuous ? 

How does Cadet de Vaux prevent the fracture of lamp glasses by heat ? 

* See Encyclop. Metropol. — Mixed Sciences, vol.i. p. 186. 
f See Treatise on Mechanics, No. 224. 



DILATATION OF LIQUIDS AND GASES BY HEAT. 291 

43. The influence of heat, as a dilating or expanding- power, 
applied to liquids, is greater than in the case of solids. But the 
degree of action which it exerts is different with respect to diffe- 
rent liquids ; so that ether is more readily expanded than rectified 
spirit, the latter is more expansible than water, and water more so 
than mercury. This might be experimentally demonstrated by 
filling the bulb of a large thermometer tube with each of these 
liquids in succession, and then presenting the bulb to a lamp at 
precisely the same distance, and observing the height to which 
the liquid would rise in each case in a given time. 

44. As different liquids undergo different degrees of expansion 
at the same temperature, so the expansibility of one liquid will 
be found to increase or diminish under variations of temperature 
in a different ratio from those which regulate the expansion of 
other liquids. This irregular effect of heat is chiefly observable 
in liquids which boil at a comparatively low temperature, as is 
the case with water ; while mercury, which requires a great de- 
gree of heat to make it boil, or become evaporated, undergoes 
nearly the same amount of expansion by the addition of any given 
quantity of heat, whether at a low or high temperature; and 
hence its utility in the construction of instruments for measuring 
heat. 

45. The influence of temperature on the bulk or dimensions of 
aeriform bodies, whether permanent or non-permanent, is more 
strikingly exhibited than in the case of the liquids or solids. This 
may be ascertained by taking a bladder half filled with air, and 
tying it so that none can escape, when, if it be held near the fire, \ 
the included air will expand till the bladder is fully distended ; 
and if while in that state it be plunged into cold water, the air 
will contract in bulk, and the bladder become flaccid. Such a 
bladder if very thin, would form an air-balloon, which would as- 
cend, when heated, to the ceiling of a lofty room, and fall down 

as soon as by the gradual cooling of the air within it the specific 
gravity of the mass was reduced below that of an equal body of 
the surrounding air. The expansibility of air by heat may also 
be demonstrated by means of the apparatus represented below. 

46. It consists of along glass tube A B, with 
a bulb at one end, and open at the other, which . 
is plunged into the jar of water C ; then on S 
heating the bulb by means of the lamp D, the 
air within the tube will become expanded, and 
issuing in large bubbles from the aperture B, 
it will rise rapidly through the water in the jar. 
On removing the lamp after a considerable por- 
tion of the air has been expelled, the water will 
rise in the tube to supply its place, as the tube 

How are liquid and solid bodies comparatively affected by increase of 
temperature ? 
What relation have the different liquids to each other in this respect ? 




292 pyroxomics. 

cools. The reapplicatloh of the lamp to the bulb at a greater dis- 
tance than before will again dilate the included air and depress 
the water in the tube ; and the liquid may be made thus to rise 
and fall alternately by cooling and heating the bulb. 

47. It is of importance to observe that airs, gases, and vapours, 
are all alike affected by given quantities of heat; that is, they not 
only all expand in the same proportion at certain degrees of tem- 
perature, but their rate of expansion under any increase of tem- 
perature is likewise uniform. In this respect it w T ill be perceived 
that gaseous bodies differ from solids and liquids; for while both 
the latter kinds of matter display the utmost dissimilarity in their 
relations to heat as an expanding power, the former always under- 
go expansion in exact proportion to the degree of temperature to 
which they are exposed. 

Instruments for Measuring Heat. 

48. The universal influence of heat on the dimensions of ma- 
terial substances affords a convenient method of estimating the 
relative quantity of heat which will produce any given effect; for 
since it appears that a certain increase of temperature will always 
be accompanied by a certain degree of expansion of bulk, it fol- 
lows, that if we can estimate correctly the degree of expansion in 
any given case, we may thence infer the amount of temperature. 
Upon this principle depends the utility of those philosophical 
instruments called Thermometers* and Pyrometers. f 

43. Among the former of these instruments is that which fre- 
quently accompanies the barometer, indicating by the expansion 
of mercury, or some other fluid, the relative temperature of the 
atmosphere, at different times or places. The mercurial thermome- 
ter consists essentially of a glass tube with a bulb at one extremity, 
and which having been filled with mercury at a certain tempera- 
ture, introduced through the open end, has been hermetically seal- 
ed Avhile full, so that no air can afterwards enter it. As the tube 
and mercury in it gradually become cooled, the inclosed fluid con- 
tracts and consequently sinks, leaving above it a vacant space or 

In what degree will the same liquid he found expanded hy equal quan- 
tities of heat when applied to it at different temperatures? 

In what class of liquids is this principle most strikingly verified ? 

How is the effect of temperature on aeriform bodies exhibited ? 

How may the ascent of a mass of heated air be visibly illustrated ? 

Explain the manner in which the expansion of air is proved by heating 
a glass bulb. 

How are the different kinds of air and vapour relatively expanded by- 
heat ? 

Of what use to science and arts is the principle of expansion ? 

Of what does the mercurial thermometer consist? 

What two points are usually established on the tube before graduating 
the scale of a thermometer ? 

* From the Greek G.=p,«:,-, hot, or &;p,«>:, heat, and tysrpov, a measure, 
f From riup, fire, and t.Ur e ev 



INVENTION OF THE THERMOMETER. 293 

vacuum, through which it may again expand on the application 
of heat. To such a tube it is necessary to add a scale showing at 
what height the mercury will stand at the temperature of freezing 
water, and what will be the rate of expansion at any other point, 
as that of boiling water, together with the amount of expansion 
at regular intervals between those two points. 

50. In what is called the centigrade thermometer, now used in 
France, the freezing point of water is marked on the scale zero ^0°) ; 
and the boiling point 100°, the intermediate space being accordingly 
divided into one hundred equal parts, regularly marked and num- 
bered ; and as the scale may be continued to any required extent, 
above or below zero, any degree of temperature may be thus as- 
certained, at least between the freezing and the boiling points of 
mercury ; and as this metallic fluid requires a far more intense 
cold than water does to make it freeze, so it will take a much 
greater degree of heat to make it boil ; and the scale may thus be 
extended in both directions. Mercury freezes at 40 deg., or 40 
centigrade degrees below zero, or the freezing point of water; and 
it boils or becomes sublimed, in vacuo, at +350 deg., that is, it 
takes a higher temperature by 250 centigrade degrees to make it 
boil than is required to make water boil. 

51. Any fluid might be employed to mark, by its relative ex- 
pansion and contraction, the temperature to which it might be ex- 
posed ; and thus sulphuric acid, water, alcohol, oil, and air, have 
been variously adopted in the construction of thermometers for 
different purposes. The invention of this useful instrument ap- 
pears to have occurred in the early part of the seventeenth century ; 
and the mode of measuring heat first employed was by observing 
the expansion of air confined in a glass tube. It is rather uncer- 
tain with whom this idea originated ; but among those who have 
laid claim to it may be mentioned Cornelius Drebbel, of Alkmar, 
in Holland, and Santo Santorio, professor of medicine at Padua, 
in Italy ; and it is not improbable that this method of discovering 
the relative effect of high or low temperature may have been in- 
dependently adopted by both those ingenious men. Drebbel, wbo 
passed some part of his life in England, in the reign of Charles I., 
certainly introduced the knowledge of the thermometer into that 
country. 

52. The original thermometer was a very imperfect instrument. 
It consisted of a glass tube with a bulb turned upward, and the 
lower portion of the stem partly filled with a coloured liquid, and 
inverted in a globular bottle partially filled with the same liquid ; 
so that the portion of air included in the bulb and upper part of 
the tube was exposed to atmospheric pressure, and therefore the 

How is the freezing point marked on the centigrade thermometer. 11 
How the boiling point ? 

At what temperature on that scale does mercury freeze ? and at what 
point does it boil- } 

By whom and at what period was the thermometer invented ? 
What was the construction of the original thermometer ? 
2 b 2 



294 PTRONOMICS. 

effect of heat on it could not be accurately appreciated. It was 
indeed merely adapted to afford a general estimate of the influence 
of temperature on the bulk of air ; much in the same manner as 
it is exhibited by the apparatus previously described.* This kind 
of thermometer was improved by the French philosopher Amen- 
tons ; and Leslie, Woiiastcn, and others, have adopted several 
modifications of the air-thermometer, as a delicate instrument for 
indicating - trifling variations of temperature; but the extreme sen- 
sibility of air to the impression of heat must ever confine its utility 
to such purposes as those just mentioned. 

53. The greatest defect in the early thermometers arose from 
the want of a regular scale of temperature, with fixed points to 
form a medium of comparison between the effects of heat as ex- 
hibited under different circumstances, or in its operation on diffe- 
rent bodies. Boyle proposed the congealing point of oil of aniseed 
for this purpose ; but Dr. Hooke with greater propriety recom- 
mended the freezing point of distilled water ; and Sir Isaac Newton, 
adopting this as the commencement of his scale, or the point zero 
(0°), he ascertained that 34° would mark the boiling point of wa- 
ter, as indicated by the relative expansion of linseed oil, the fluid 
which he used to fill his thermometer.! 

54. The discover}" of two fixed points for the thermometrical 
scale contributed vastly to the improvement of the instrument ; 
but that of Newton was rendered imperfect by the nature of tfie 
inclosed fluid, which did not move freel} 7- within the tube, and by, 
the inconvenient length of the degrees of the scale. Hence other 
men of science employed themselves in contriving by various 
methods to augment the utility and accuracy of this instrument. 
Reaumur, in France, invented a thermometer filled with tinged 
spirit of wine, with a scale divided into 80 degrees between the 
freezing and the boiling points of water. But as spirit of wine boils 
at a lower temperature than water, and as it could afford no indication 
of any degree of heat beyond its own boiling point, on this ac- 
count, the spirituous fluid was exchanged for mercury; and such 
a mercurial thermometer, with Reaumur's scale, was in general 
use in France till the period of the revolution, when it was super- 
seded by the centigrade thermometer, already noticed. 

55. The employment of mercury as the most suitable fluid for 
the thermometer is usually attributed to Fahrenheit, a native of 
Dantzic, who settled at Amsterdam as a philosophical instrument- 
maker; and his instruments having the merit of great accuracy 

Who are among the improvers of this instrument ? 

"What defect existed in the original thermometers p 

What limits the useful application of the air thermometer? 

What peculiar disadvantage had the thermometer of Newton? 

In what manner did Reaumur divide his scale ? 

What scale has superseded that of Reaumur in France ? 

* See above, No. 46. 

f See Cotes's Hydrostat. Lect. Appendix, No. II. 



DIFFERENT KINDS OF THERMOMETERS. 2S5 

and neatness of execution, became much sought after, and his 
name has been permanently connected with that form of the 
thermometer, now generally used in England, Holland, and the 
United States. It appears, however, from the statement of Boer- 
haave, that the improvement of the thermometer, so far as relates 
to filling it with mercury, and fixing on the peculiar scale denomi- 
nated after Fahrenheit, ought rather to be ascribed to Olaus Roe- 
mer, a Danish philosopher, to whom we owe the discovery of the 
velocity of light.* The peculiarity of this scale is, that it does 
not commence at the freezing point of water, but descends much 
below it. 

56. It is usually stated that Fahrenheit obtained the point, 
whence he commenced the graduation of his thermometers, by 
producing artificial cold from the mixture of common salt and 
snow; but from the authority just cited, it appears that zero of 
Fahrenheit's, or rather Roemer's scale, was derived from the 
lowest degree of temperature, or greatest cold which had been 
observed in Iceland, which was fixed on from an erroneous sup- 
position that this was the extreme of low temperature which was 
ever likely to become the object of philosophical investigation. 

57. Among the numerous modifications of the thermometer pro- 
posed by ingenious men, as adapted to the general purpose of in- 
dicating variation of temperature, the only one besides the preced- 
ing which requires to be here noticed, is that of J. Delisle, member 
of the Academy of Sciences, at St. Petersburg. It differs prin- 
cipally from other instruments in having a scale, the graduation 
of which commences at the boiling point of water, and is reckoned 
downwards : the distance to the freezing point being divided into 
150 degrees. Its use is nearly confined to the Russian empire, 
where it is generally adopted by men of science. 

58. As the centigrade thermometer, originally invented by 
Olaus Celsius, of Upsal, in Sweden, and that of Fahrenheit, are 
at present commonly used in registering observations on tempera- 
ture, in France and Great Britain, while those of Reaumur and 
Delisle have been employed by several eminent philosophers in 
making and recording their peculiar observations, it becomes re- 
quisite that the means should be afforded for ascertaining the 
relative value of degrees of temperature, according to either of 
these scales, and of converting any given number of degrees be- 
longing to one scale into degrees belonging to that with which we 
are most familiar. Fahrenheit's scale, commencing at zero (0°), 
ascends to 32° the freezing point of water, and thence to 212°, the 

In what countries is the scale of Fahrenheit chiefly used ? 
To whom belongs the application of mercury, and the original use of 
the scale adopted by Fahrenheit ? 

How did Roemer actually obtain the zero of his instrument? 
Where did Delisle commence the graduation of his thermometer ? 
Where and by whom was the centigrade thermometer invented ? 

* Boerhavii Elements Chemise, t. i. p. 720. 



296 



PYROXOMICS. 



boiling point; so that there are 180 degrees, in the scale, between 
these fixed points. 

59. The following table exhibits corresponding- numbers of the 
several scales of Fahrenheit, Reaumur, Delisle and Celsius, or 
that of the centigrade thermometer, from a temperature 12 degrees 
above the boiling point, Fahrenheit, to 96 degrees below zero. 



Fahr. 


Reaumur 


Delisle 


Centigrade 




1224 


85 3-9 


10 


106 6-9 


212 


80 





100 


Boiling point of water. 


192 


71 1-9 


16 4-6 


88 8-9 




160 


56 8-9 


43 2-6 


71 1-9 




128 


42 6-9 


70 


53 3-9 




96 


28 4-9 


96 4-6 


35 5-9 


Blood heat. 


64 


14 2-9 


123 2-6 


17 7-9 




32 





150 





Freezing point of water. 





14 2-9 


176 4-6 


17 7-9 




32 


28 4-9 


203 2-6 


35 5-9 




39 


31 5-9 


209 1-6 


39 4-9 


Freezing point of mercury. 


64 


42 6-9 


230 


53 3-9 




90 


54 2-9 


251 4-6 


67 7-9 


( Greatest known degree 
( of cold. 


96 


56 8-9 


256 4-6 


71 1-9 





60. Hence it will appear, that 1° of Fahrenheit's scale is equal 
to 4-9° of Reaumur's, 5-6° of DelisWs, and 5-9° of the centigrade 
scale. Therefore in order to convert any number of degrees of 
Reaumur into corresponding degrees of Fahrenheit, the given num- 
ber must be multiplied by 9 and divided by 4, and if it be a number 
above zero, 32 must be added to the product, and the amount will 
be the degree required ; but if the number be below zero of Reau- 
mur, and above zero of Fahrenheit, that is any number less than 
14 2-9, the product must be subtracted from 32; and if it be a 
number below 14 2-9, 32 must be subtracted from the product, 
to obtain the degree required. In the same manner the correspon- 
dence between degrees of the centigrade scale and that of Fahrenheit 
may be ascertained, only the given number of centigrade degrees 
must be multiplied by 9 and divided by 5. To convert degrees of 
Delisle into degrees of Fahrenheit, the given number must be mul- 
tiplied by 6 and divided by 5, and the product subtracted from 
212 will be the number required; but if the number be below 
zero of Fahrenheit, or 176 4-6 Delisle, 212 must be subtracted 
from the product; and if the number required be degrees of Delisle 



Name the boiling- points on the four therraometric scales. 

What are the freezing points on them respectively ? congealing point 
of mercury ? greatest known degree of cold ? 

What rules can be given for converting degrees of Reaumur, Celsius, 
and Delisle respectively into those of Roemer or Fahrenheit ? 



wedgwood's pyrometer. 29? 

above zero, 212 must be added to the product to obtain fLe number 
required, denoting the corresponding degree of Fahrenheit. 

61. The mercurial thermometer is the most convenient instru- 
ment for measuring any degree of temperature between 644 deg. 
Fahrenheit, at which the liquid boils, and 39 deg. below zero, at 
which it freezes. For the mensuration of more intense degrees 
of cold, a thermometer maybe employed filled with alcohol, tinged 
red by means of alkanet-root ; for that fluid, when otherwise per- 
fectly pure, will remain uncongealed at a temperature much lower 
than that at which mercury freezes. 

62. As there is no known liquid that continues unevaporated at 
a higher temperature than mercury, the relative effect of very high 
degrees of heat is usually estimated by the alteration of bulk that 
takes place in solid bodies. Heat generally expands substances 
of all kinds ; but Mr. Wedgwood observed that fine porcelain clay 
becomes contracted by exposure to great heat ; and he found, on 
investigation, that pieces of pure clay carefully dried, and then 
exposed to a red heat in a furnace, exhibited a sensible degree of 
contraction, which remained when they "again became cool ; and as 
it further appeared that the contraction proceeded with the aug- 
mentation of heat, till vitrification took place in the clay, he con- 
ceived the idea of forming a pyrometer, or measurer of heat, con- 
sisting of a number of test-pieces of prepared clay, in the shape 
of small flattened cylinders, and a scale composed of brass rods 
i inch square, and 2 feet long, fixed to a brass plate, obliquely 
inclining inwards, so as to be somewhat nearer together at one 
end than at the other, and marked with a scale of equal parts, 
commencing at the wider extremity. 

63. As the contraction of the clay pieces is permanent, a fresh 
one must be used for each trial, which is to be made by exposing 
one or more test-pieces to the heat, the intensity of which is to be 
ascertained, and when thus heated and again cooled, the contrac- 
tion that has occurred is to be measured by sliding the piece be- 
tween the brass rods so far as it will go, and observing the dimi- 
nution of bulk as indicated by the scale, all the pieces being 
adapted exactly to fit the widest part of the scale before their ex- 
posure to the heat, the estimation of which is the object of experi- 
ment. The seemingly anomalous effect of heat on which the 
property of this instrument depends may be accounted for, as the 
result of the concentration of the particles of the clay by the more 
intimate union of the argillaceous and siliceous earths of which 
it is composed. 

64. Each degree of Wedgwood's scale is equivalent to 130 de 

Within what limits may the mercurial thermometer he employed ? 

In what manner has it been usual to estimate very high degrees of 
heat ? On what observation did Wedgwood found the construction of 
his pyrometer? Can Wedgwood's standard pieces be repeatedly used 
for the same purpose ? 

In what manner is the contraction of the porcelain pieces to be ac~ 
counted for ? 



298 



PYRONOMICS. 



grees of that of Fahrenheit ; and the former commences at 1077°.5 
of the latter scale. The mode adopted for instituting- a compari- 
son between the two scales was by observing the expansion of a 
pyrometric piece of silver and of a test-piece of clay, as relatively 
exhibited at 50 deg. and 212 deg. Fahrenheit, and at higher tem- 
peratures as indicated by the brass scale. Having thus obtained 
a common measure of high temperature, the inventor of the py- 
rometer proceeded to make various researches concerning the 
melting points of metals, and other subjects ; and it maybe stated 
as the result of his inquiries, that the greatest heat he ever pro- 
cured was from an air-furnace, amounting to 160 deg. Wedgwood, 
equal to 21,877 deg. Fahrenheit. 

65. Doubts have been started whether the contraction of clay 
affords a uniform measure of temperature ; and the more recent 
investigations of M. Guy ton Morveau, and Mr. Daniell, render it 
very probable that Wedgwood formed his comparison of the py- 
rometric and the thermometric scales on an erroneous assumption 
relative to the melting point of silver. Hence the calculations 
grounded on experiments made with his pyrometer are not to be 
absolutely depended on ; though the instrument is well adapted to 
the exigencies of the potter, as affording the means of ascertaining 
the heat of furnaces with sufficient exactness for many purposes. 

66. A great many pyrometers have been invented by various 
experimentalists, exhibiting different methods for measuring, with 
more or less accuracy, the relative expansion of bars or wires of 
iron, or of some other metal.* 

Several of these are con- 
structed on the principle of 
that represented in the mar- 
gin, in which a bar of metal, 
A, may be so placed, that 
when expanded by the heat 
of a lamp B, one extremity 
will press against a lever 
and cause an index, C, to 
~^*~' move along the graduated 
arc D ; and by means of such a pyrometer, the effect of heat, ap- 
plied in the same manner, for a given length of time, to bars of 
different metals having the same length and diameter, may be as- 
certained. 

67. Mr. Daniell contrived a pyrometer adapted to measure the 

How did Wedgwood unite the indications of his scale to those of the 
common thermometer ? What reliance is to be placed upon it as an ab- 
solute measure of temperature ? To what practical purpose may it be 
usefully applied ? On what principle have pyrometers generally been 
constructed ? 

* For descriptions and figures of a number of pyrometers, invented 
by ingenious British and foreign philosophers, see a Treatise on the 
Thermometer and Pyrometer, published by the Society for the Promo- 
tion of Useful Knowledge. 







METALLIC PYROMETERS. 



299 



expansion of a rod of plantina, made to move an index over a 
dial-plate divided into 360 degrees, each equal to 7 degrees of 
Fahrenheit. He published an account of experiments made by 
means of his pyrometer, the result of which may be subjoined, as 
being probably the most exact yet published relative to the effects 
of high temperatures.* 

Melting point of tin . 

bismuth . 

lead 

Boiling point of mercury 
Melting point of zinc 
Red heat visible in full daylight 
Heat of a common parlour fire , 
Melting point of brass . 
silver . 



copper 
gold _ . 
cast iron 



Daniell. 


Fahrenheit. 


. 63° 


441° 


66 


462 


. 87 


609 


92 


644 


. 94 


658 


140 


980f 


. 163 


«141 


267 


1869 


319 


2233 


364 


2548 


370 


2590 


497 


3479 



68. Pyrometers, or rather metallic thermometers, suited for mea- 
suring with great accuracy small variations of temperature, have 
been constructed by contemporary artists, among whom may be spe 
cified Breguet and Frederic Houriet, of Paris, and Holzmann, o» 
Vienna. 

In the prosecution of delicate experiments on the influence ol 
temperature, those thermometers may be most advantageously em- 
ployed in which the effect of heat is exhibited by the expansion 
of air, included in a small tube with a scale annexed. 

69 Among the more recent and useful forms of such instruments, 
the more important is that called the Differential Thermometer, 
invented by Leslie, and described in his "Experimental Inquiry 
into the Nature of Heat." 

It consists of two bulbs or glass spherules A 
and B, connected by the tube C D E F, bent 
twice at right angles, and supported by a wooden 
stand G. Within the tube is a small quantity 
of coloured sulphuric acid ; and when a heated 
substance is brought near to the bulb A, the in- 
closed liquid recedes, and rises on the opposite 
side, where its relative height, as indicated by 
the scale attached to the tube E F, will show 
the degree of expansion of the air in the tube 
and bulb A C D. One of the principal advan- 

* Subsequent to the publication of this table, Mr. Daniell published 
others, differing very considerably from these. Besides which, Mr. 
Prinsep of Benares, in the East Indies, has published the results of some 
experiments with an air pyrometer, and the editor of this work has made 
numerous experiments with his steam pyrometer, described in the Amer. 
Jour, of Science and Arts, vol.xxii. p. 96.* — En. 

t Probably too low. — En. 




300 pyroxomics. 

tages attending the use of this instrument is its not b '-ing liable to 
error from changes in the temperature of the atmosphere ; for the 
heat of the surrounding air must act on both bulbs in the same 
manner, therefore when a heated object is applied to one bulb only, 
the whole effect produced by it will appear 'from the different 
amount of expansion of the enclosed air ; or if a cold object be 
applied the effect will be equally obvious from the different cov 
traction which takes place ; and hence the instrument is named 1 
differential thermometer. 

70. The actual amount of expansion that takes place in different 
bodies raised to the same temperature is, as already observed, by 
no means equal. According to recent experiments of Herbert o& 
the expansion of solids by heat, it appears that rods of gla^s and seve- 
ral metals, of the same length at the freezing point of water, were 
variously extended at the boiling point. Thus the longitudinal 
dimensions of each being supposed divisible into 100.000 parts, at 
32 deg. Fahrenheit, each substance, at 212 deg. was augmented 
in the following proportions : 

Platina 85 parts. 

Glass 86 

Gold 94 

Iron 107 

Copper .... 156 

Brass 172 

Silver 189 

Tin 212 

Lead 262* 

71. Liquids also expand unequall}' at different temperatures, 
and different liquids are variously affected by the same tempera- 
ture. The irregular expansion of liquids interferes with the re- 
sults of experiments made by means of common thermometers; 
out mercury as exhibiting more uniformity in its rate of expansion 

What substance did Daniell adopt for the measure of high tempera- 
tures ? 

What temperature did he assign for that of redness in daylight ? 

What did he obtain for the melting point of silver ? 

What for that of cast iron ? 

What species of experiments may be advantageously prosecuted with 
the air thermometer ? 

What liquid is employed in the differential thermometer ? 

What is one of the chief advantages of this instrument ? 

Are all bodies equally adapted to the formation of instruments to mea- 
sure heat by expansion } Why ? 

By how many millionths of its length, taken at the freezing point, will 
a bar of platina be found expanded when raised to the boiling point of 
water ? a bar of iron ? of silver ? of lead ? 

How are liquids affected by equal augmentations of temperature in dif- 
ferent parts of the scale ? 

* Vieth's Elem. of Nat. Philos. (Germ.), p. 314. 



RATE OF EXPANSION OF LIQUIDS. 301 

than other fluids, as water or alcohol, is better adapted than they 
are for thermometrical investigations. Indeed the more readily 
liquids evaporate under the influence of heat, the greater will be 
their dilatation, when it takes place without change of form; and 
therefore ether and alcohol expand more in proportion at relatively 
high than at low temperatures, and mercury, which requires a 
great heat to make it boil, increases its rate of expansion more 
slowly. 

72. The following table of the expansions of liquids is derived 
from the researches of Mr. Dalton, who ascertained that an eleva- 
tion of temperature from the freezing to the boiling point of water 
would cause an increase of volume in the ensuing proportions. 



Mercury as 1 to 


. 0-0200 


Water .... 


0-0466 


— — saturated with salt 


. 0-0500 


Sulphuric acid . 


0-0600 


Muriatic acid 


. 0-0600 


Oil of turpentine 


0-0700 


Ether 


. 0-0700 


Fixed oils 


0-0800 


Alcohol .... 


. 0-1100 


Nitric acid 


0-1100 



73. Aeriform fluids, as before stated, all dilate alike, and undergo 
uniform degrees of expansion at different temperatures. This pro- 
perty of gases and vapours depends on their being destitute of co- 
hesian, so that the influence of heat operates on them simply and 
independently, its effect not being modified by any opposing power, 
as in the case of solids and liquids. From the experiments of 
Gay Lussac in France, and those of Dalton in England, it appears 
that all elastic fluids, whether airs or vapours, when raised from 
the temperature of 32 deg. Fahrenheit to 212 deg., become ex- 
panded nearly in the ratio of 100 to 137.5 ; or 100 cubic inches of 
gas at the freezing point of water, if heated to the boiling point, 
would be augmented in bulk to 137^ inches. Hence the expan- 
sion of volume for each degree of the centigrade thermometer 
would be 0.375, or reckoning the bulk at zero as 1 (unity), the 
augmentation for each degree would be 0.00375. Dalton estimates 
the increase of bulk for every degree at 0.00372, which would be 
nearly equivalent to 0.00208 for each degree of Fahrenheit's ther- 
mometer. 

How is the rate of dilatation related to the boiling 1 point of liquids ? 

What examples prove the truth of this principle ? 

How much is mercury expanded by the addition of ISO degrees Fah- 
renheit to its temperature at the freezing point? 

On what property of gases is their uniform rate of expansion supposed 
to depend ? 

How much is the bulk of a gas enlarged by heating it from the freez- 
ing to the boiling point ? 

What will be the rate for one degree ? 
2C 



302 PYRONOIMCS. 

74. Thus it appears that the density of substances generally 
bears a certain relation to their temperature, being- augmented by 
cold and diminished by heat, or in other words, contracted by ex- 
posure to a low temperature and expanded at a high cempera- 
ture. So far as we can judge from experiment, the maximum 
density of solid bodies must be at the lowest temperature which can 
be produced. And the same maybe stated with respect to liquids 
which are not susceptible of being solidified by cold, or frozen. 
But this does not always hold good with regard to freezing or 
congealing liquids ; and water is especially remarkable for its pro- 
perty of expanding in the act of congelation, whence, as is generally 
known, vessels are liable to be burst in winter by the freezing of 
aqueous liquors contained in them ; and loose ice is always seen to 
float on water, in consequence of its inferior specific gravity. 

75. From the researches of Deluc and others, it appears that 
pure water acquires its maximum density at the temperature of 
40 deg. Fahrenheit, whence, if the cold be increased, it expands 
till it reaches the freezing point 32 deg. ; so that ice at 32 deg. has 
the same specific gravity as water at 48 deg. But for this pro- 
perty of water, large ponds and lakes exposed to intense cold 
would not merely be frozen over, as is usual in the winter season, 
but they would become entire masses of solid ice. For ice once 
formed, if heavier bulk for bulk than the water beneath it, would 
sink to the bottom of the pond or lake, and remain there to be 
augmented by fresh descending portions, as long as a frost lasted ; 
but its relative levity causes it to continue on the surface of the 
liquid which it protects in some degree from the cold atmosphere, 
and congelation consequently proceeds more slowly. 

76. This remarkable property of liquids near the point of con- 
gelation is certainly not, as generally stated, peculiar to water, for 
other aqueous fluids are affected in the same manner ; and there 
is reason to believe that metallic and other substances, which have 
been melted by exposure to great heat, contract in cooling only to 
a certain point, and then expand, like water, so that the density 
of a mass of metal just become solid will be inferior to that of 
the same metal a few degrees above that at which it takes the 
solid form. 

77. Reaumur states that iron, bismuth, and antimony, are more 
condensed just before they become solid than afterwards; and he 
observes that hence figures cast in iron are correctly marked, from 
the expansion of the metal in cooling, which causes it to press 
into the most minute indentations of the mould. Sulphur exhi- 
bits the same appearances, when used for taking impressions of 

What must be the maximum density of solid bodies ? 

Why are closely corked bottles burst when their liquid contents freeze ? 

Why does ice not sink to the bottom of cold water ? 

Is the property of expanding near the freezing point confined to a sin- 
gle liquid ? 

What causes the accuracy with which iron and other metals fill the 
moulds, and thus yield " sharp castings?" 



LATENT HEAT. 303 

medals ; and it is probable that all bodies capable of fusion by heat, 
would, under similar circumstances, be found to have less density 
at the point of solidification than just before the commencement 
of that process. As to the cause of this phenomenon, the most 
probable conjecture is that of De Mairan, who, in his Treatise on 
Ice, ascribes the expansion of freezing water to the new arrange- 
ment of its particles consequent to crystallization, so that the 
minute and still invisible intervals between the molecules of the 
mass are larger or more numerous in ice than in water 8 deg. above 
the freezing point. But this interesting topic demands further 
investigation. 



Latent Heat, and its Influence on the Forms of Bodies. 

78. No indication is afforded by the thermometer of the abso- 
lute quantity of heat which any substance may contain, but merely 
of the amount of free or sensible heat capable of producing a cer- 
tain degree of expansion in a column of mercury. If a quantity 
of ice at 32° Fahrenheit be placed in a jar set ir> a basin of water 
considerably heated, the ice will gradually melt, absorbing heat 
from the water through the sides of the jar ; but though it must 
thus receive successive portions of heat, they would produce no 
effect on a thermometer within the jar, the mercury in which would 
remain at the freezing point till all the ice became dissolved. So 
that any quantity of heat thus absorbed by ice in the act of thaw- 
ing would become combined with the liquid, constituting what is 
termed latent heat, as not being appreciable by the thermometer. 

79. Different bodies require different quantities of heat to raise 
them to the same therm ometrical temperature, or at least they are 
differently affected by exposure to the same temperature. Thus, 
if a quart of water and a quart of olive oil be removed, from a 
room in which the heat of the air is but 40° Fahrenheit, to another 
room heated to 80°, both liquids would gradually acquire the lat- 
ter degree of heat, as might be ascertained by placing a thermome- 
ter in either liquid. But the oil would be perceived to have become 
raised to the temperature of 80° much sooner than the water ; and 
hence it has been inferred that a smaller quantity of heat is re- 
quired to produce an augmentation of 40° of temperature in the 
former liquid than in the latter. As oil becomes heated more 
speedily, under the same circumstances, than water, so likewise 
it cools faster than water ; as would appear on reversing the pre- 
ceding experiment. 

To what does De Mairan attribute the diminution of density in bodies 
at their points of congelation ? 

To wbat is the indication of a thermometer limited ? 

In what change of a solid body is sensible converted into latent heat ? 

When equal quantities of different bodies are exposed to a change of 
temperature, what difference may we expect to find among them while 
undergoing that change ? 

Exemplify this in the case of two liquids. 



> 



304 PYRON03IICS. 

80. When equal quantities of the same body at different tem- 
peratures are mixed, the temperature of the mixture will be at the 
medium between those of the two portions : thus a pint of water 
32° added to another pint at 98° would produce a quart of water 

,, at 65° ; half the difference between the temperature of the hot 
-x water and the cold (33°) having' been taken from the former and 
added to the latter. But the result is very different when dissimi- 
lar bodies at different temperatures are mingled : for if one pound 
of water at 156° be mixed with one pound of mercury at 40°, the 
common temperature will be 152°, instead of 98°; the medium 
temperature, which would have been that of the mixture if water 
had been used instead of mercury. 

81. From this experiment, it appears that the water gives up 
4° of its heat to raise the mercury 112°; whence it has been 
concluded that water has a greater capacity for heat than the me- 
tallic fluid, in the ratio of 112 to 4, or 28 to 1. If the experi- 
ment be reversed, by mingling- one pound of mercury, at 156° 
with one pound of water at 40°, the common temperature will be 
44° ; the mercury having - been deprived of 112° of its heat, while 
the water has acquired but 4°. A pound of gold at the tempera- 
ture of 150° added to a pound of water at 50° will raise the tem- 
perature of the liquid but 5°, while it will lose 95°, the common 
temperature being 55°. Hence the relative capacity for heat of 
gold and water would be as 5 to 95° ; so that the capacity of 
water for heat must be 19 times greater than that of g'old. But 
the results of different experiments on specific heat, vary con- 
siderably from each other. Thus Lavoisier and Laplace make 
the specific heat of mercury .029, water being 1.000 ; Petit and 
Dulong make it .033 ; Kirwan .033, and Dalton .0357 ; these dif- 
ferences are, probably, to be attributed to the different methods of 
conducting the experiments. 

82. Several attempts have been made to ascertain with greater 
precision the quantities of heat given out by different substances 
under various circumstances. Lavoisier and Laplace constructed 
for this purpose an instrument called a calorimeter, adapted to 
measure the quantity of ice melted by different bodies, in the pro- 
cess of cooling from any given temperature to 32° Fahrenheit. 
Various precautions were employed to prevent the access of exter- 
nal heat, while the cooling process was going on, and for estimat- 
ing with exactness the quantity of water produced by the fusion 
of the ice within the body of the instrument. 

83. After having determined from experiments with the calori- 
meter, that the heat absorbed by one pound of ice in melting would 

What will be found to take place on mixing equal quantities of the 
same body at different temperatures ? 

What two liquids afford a striking illustration of this point ? 

What term is applied to signify the relative power which different bo- 
dies possess of absorbing heat ? 

What method was adopted by Lavoisier and Laplace to measure the 
heat given out in cooling ? 



SPECIFIC HEAT OF BODIES. 305 

be sufficient to raise an equal weight of water from 32° to 157°, 
or 135 degrees,* the French philosophers proceeded to ascertain 
the relative quantities of heat evolved by different bodies, in cool- 
ing, through a certain number of thermometrical degrees, as also 
in other processes. But the results obtained by means of this in- 
strument are liable to inaccuracy from various causes, which render 
it difficult, if not impossible, to collect the whole of the water 
produced from the melting ice ; for it has been rendered probable 
that a part of the water thus formed may sometimes be congealed 
again in its passage through the lower part of the calorimeter, so 
that the quantity obtained will afford no certain measure of the 
effect of the evolution of heat from the body under investigation. 

84. Other experimentalists have therefore had recourse to dif- 
ferent methods of appreciating the specific heat of various sub- 
stances. Count Rumford invented a calorimeter, for estimating 
the quantity of heat given out, in the cooling of heated bodies or 
other processes, by observing the increase of temperature in a 
bod)'' of water, adapted to receive the heat evolved from the sub- 
jects of his experiments. On a similar principle is founded the 
method of ascertaining the capacity for heat, or as it is also term- 
ed the specific heat of gaseous fluids, employed by MM. Delaroche 
and Berard. 

85. Another mode of conducting researches of this nature, con- 
sists in noticing the time required to cool any substance through 
a certain range of temperature, as indicated by the thermometer, 
and comparing its rate of cooling with those of other substances. 
The experiments of Leslie, and those of Dalton, on the specific 
heat of different bodies were thus conducted; and a similar plan 
was pursued by MM. Dulong and Petit in their experiments on 
metals. 

86. All these methods of operating are more or less liable to 
objection ; and the results thus obtained can only be regarded as 
affording some approximate estimates concerning the relative influ- 
ence of temperature on different bodies. Two other methods of 
determining specific heat, have recently been put in practice. The 
first, is that of Weber, who measured the heat given out by 
stretching a bar of metal, and observing how much the elasticity 
had been diminished by the loss of heat. The second, is the me- 
thod of evaporation, employed by the editor of this work, and 

What quantity of heat did they find to become latent by the melting of 
ice ? 

To what objection is the calorimeter exposed ? 

How did Rumford attempt to determine specific heats? 

To what purpose did Delaroche and Berard apply this method ? 

What method was employed by Dalton, Leslie, Dulong, and Petit for 
the determining- of specific heats ? | 

What other modes of arriving at the same object have been adopted ? 

* Dr. Black estimated the heat required to melt a given quantity of 
ice as equal to that which would raise the temperature of the same weight 
of water from 32 to 162 or 140 decrees. 



306 PYRONOM1CS. 

described in the American Journal of Science,* together with 
formulae for calculating the specific heats. 

87. As the general effect of heat is to cause an increase in the 
volume of bodies exposed to its action, producing expansion com- 
monly in all directions, but in different degrees according to the 
nature of the substance on which it operates, an estimate of the 
quantity of heat thus operating, or rather of the amount of the 
effect thus produced, may in this manner be obtained ; and the in- 
struments adapted for measuring heat on this principle have been 
described. But, as already stated, important, changes may be 
caused in bodies by the addition or abstraction of heat without 
affecting the thermometer in the usual manner; thus solids b} r ex- 
posure to heat may be converted into liquids, and the latter, when 
heated, boil or become evaporated, or altered from the liquid to the 
gaseous or aeriform state. It was by observing the dissimilar effect 
of heat on given portions of ice and water, both at the temperature of 
32°, being placed in equally advantageous circumstances for receiv- 
ing heat, that Dr. Black was led to form his theory of latent heat, as 
the cause of the liquefaction and vaporization of different bodies. 

88. It may be stated as a general principle, deduced from nu- 
merous experiments, that when any substance becomes liquefied 
or melted by heat, a quantity of heat appears to be absorbed by 
that substance in the process of fusion, which cannot be appre- 
ciated by the thermometer; though the depression of temperature 
in bodies placed in contact with the melting substance is found to 
be very considerable. Thus water may be frozen hy placing a 
small bottle partly filled with that liquid in a basin containing 
pounded ice or snow mixed with the salt called muriate of lime"; 
and supposing the temperature of the water to be 52°, or 20° 
above the freezing point, it will gradually give out heat till con- 
gelation takes place, and the quantity of heat which thus escapes 
from it will be absorbed by the frigorific mixture of snow and salt, 
which will progressively melt or become liquefied, but will retain 
the same thermometrical temperature so long as any part of the 
mass continues undissolved. 

89. On this principle depend -the artificial modes of reducing 
liquids to the solid state, by means of freezing mixtures, which 
usually consist of mineral acids or powdered neutral salts, mixed 
with snow. Analogous effects will be observed when fusion 
takes place at a high temperature. Thus spermaceti melts at 

What effect, besides expansion, takes place in bodies by additions of 
heat ? 

What first led to the formation of Black's theory of latent heat ? 

What general principle is applicable to the heat of bodies undergoing 
liquefaction ? 

Explain this principle in the process of freezing water by frigorific 
mixtures. 

At what point would spermaceti remain stationary when exposed in its 
solid state to the effect of heat ? 

* Vol. liii. p. 279. 



ABSORPTION OF HEAT DUMNG THE MELTING OF SOLIDS. 307 

the heat cf 112°, which temperature it will retain as long- as any 
portion remains solid ; so that a person might dip a finger into the 
melting mass while fragments continued undissolved, but when 
the fusion was completed, any addition would raise the thermome- 
ter above the melting point. Tin becomes fused at 442°, and lead 
at about 602°, and at those temperatures respectively, tne metals 
would remain during the process of fusion; but after it was com- 
pleted, they might be raised to a red heat. And lead, melted and 
then made red hot, in a crucible, would immediately be cooled 
down to its melting point by throwing into it a piece of solid lead.* 

90. As absorption of heat or diminution of temperature in sur- 
rounding bodies always takes place when a solid substance is 
melted or changed to the liquid state, so heat is given out when the 
contrary change occurs of a liquid into the solid state. If a strong 
solution of Glauber salt (sulphate of soda), made with hot water 
be poured into a phial, and corked up while warm, provided it be 
left quite undisturbed, the salt will remain dissolved when below 
the temperature at which it would otherwise crystallize ; then on 
suddenly opening the bottle a mass of crystals will be immedi- 
ately formed, and their production will be accompanied with an 
elevation of temperature easily perceptible by the hand applied to 
the outside of the bottle. When water is poured on quicklime it 
loses its liquid form, and, entering into combinations with the cal- 
careous earth, constitutes the pulverulent solid called slaked lime, 
giving out the same time abundance of heat, a great part of which 
is carried off by a portion of the water rising in the form of misty 
vapour. 

91. When liquids are exposed to heat they become converted 
more or less readily into aeriform fluids; thus water is changed 
into steam, and ether and alcohol into inflammable vapours; and 
generally all liquids, heated without being decomposed, assume 
the gaseous form at certain temperatures, and are condensed to 
the liquid state again by exposure to cold. Different liquids re- 
quire different degrees of temperature in order to their conversion 
into the form of vapour. Water boils or becomes evaporated at 
212 deg., while alcohol enters into ebullition at 173^ deg., and 

How long would it retain this temperature ? 

What is the melting point of tin ? what, that of lead ? 

What phenomenon presents itself when liquids are converted into solids? 

What causes the heat which is observed in the process of slaking lime ? 

What effect of heat follows the exposure of liquids to its continued in- 
fluence i> • 

At what temperatures does boiling or vaporization take place in water ? 
in alcohol ? in ether ? 

* An important investigation of the latent heats of tin and lead, and 
of various alloys of those and other metals, has been made by M. Hud- 
berg, and will be found in the Annales <le Chym. et de Phys., vol. xlviii. 
p. 353, in which he has shown that alloys have two stationary points, un- 
less mixed in certain proportions, probably those in which they form 
complete chemical compounds, and leave no excess of either ingredient. 
—En. ' ' 



308 PYRONOMICS. 

ether at 100 deg. But similar changes take place to a certain 
extent at almost any temperature; for all kinds of aqueous liquids 
slowly evaporate when exposed in shallow masses at the coldest 
season of the year; and spirituous or ethereal liquids'cannot be 
preserved long in that state at ordinary temperatures except in 
closely-stopped vessels. 

92. Oily and saccharine liquids do not very readily evaporate 
in cold weather, but they also become dissipated through the air 
after longer exposure than those of a more volatile kind. This is 
a wise provision of nature, for if water obstinately retained its 
liquid form at all temperatures below 212 deg., the moisture that 
fell to the earth in the state of rain would never be evaporated 
during the hottest summers; and abundant inconvenience would 
arise from the presence of liquids which are now removed more 
or less speedily at all seasons, through the agitation of the air. 

93. Evaporation at low temperatures takes place from the sur- 
faces of solids as well as from those of liquids. Even ice and 
snow may be observed to diminish in quantity from evaporation 
during the continuance of a frost. Some interesting experiments 
on this subject were made in the winter of 1814-15. On the 
eastern coast of Lake Winnepie, latitude 52 deg. N. November 
28, 1814, Mr. Holdsworth hung up a disk of ice, 2 inches thick, 
weighing 20 lbs.; on the 14th of February it had lost 17 oz., the 
highest temperature in the interval being 23 deg. Fahrenheit. The 
experiment was continued till the 31st of March, when the 
entire loss of weight of the ice by evaporation amounted to 4lbs. ; 
and though the temperature on the 26th and 28th of February had 
been as high as 36 deg. during more than two hours each day, no 
dropping took place from the ice, nor was any moisture percepti- 
ble on its surface. February 16th 1815, snow was suspended in 
a crape bag or handkerchief, which, together with the snow, 
weighed 30 oz. In ten days it had lost 2 oz. ; and in nine days 
more an additional 2 oz. ; on the 14th of March, the total loss was 
6 oz., or one-fifth of its weight in twenty-six days ; the crape 
continued dry during the whole period.* Hence it appears that 
a very considerable amount of evaporation takes place from solid 
ice, when the temperature of th° atmosDhere ^s below that of 
freezing water. 

94. Among those circumstances which materially affect the 
evaporation of liquids, one of the most important is atmospheric 

Will evaporation always require the same temperature as vaporization? 
What would be the consequence, were the law of nature different from 
what it actually is in this particular ? 

What bodies other than liquids evaporate at low temperatures ? 
What experiments are related in connexion with this subject ? 
What interesting general conclusion may be drawn from them ? 
What circumstance materially affects the rate of evaporation ? 

* Journal of Science, &c, edit, at Royal Institution, vol. ix. pp. 423, 
424. 



ABSORPTION OF HEAT DURING EVAPORATION. 



309 



pressure. All liquids readily become evaporated in a highly rare- 
fied medium. Mercury is sublimed with a small degree of heat 
in the vacuum formed in the upper part of a barometer tube ; and 
water may be made to boil in an exhausted receiver of an air-pump 
at a temperature much inferior to that at which ebullition takes 
place under common circumstances. In the same manner the 
boiling point of water becomes lowered, in proportion to the rare- 
faction of the air, in ascending high mountains ; and in general the 
boiling points of all liquids will vary in some degree according to 
the pressure of the atmosphere, as indicated by the barometer. 

95. Ether, when placed under an ex- 
hausted receiver, rapidly evaporates. It 
may thus be made to boil while water \ 
placed in contact with it freezes. To ex- 
hibit this phenomenon, a small flask, B, 
must be procured, made of thin glass, 
and nearly fitting into a bell-shaped drink- 
ing-glass, C, as represented in tbe figure. 
Ether must be poured into the glass, and 
water into the flask, so that both liquids 
may stand at the height of the dotted 
line, A D, and the apparatus thus arrang- 
ed is to be placed under the receiver of 
an air-pump, on working which the ether will boil or be converted 
into vapour; and as it requires heat for this purpose, it will absorb 
it from the containing vessels and the water which it surrounds, 
and the latter liquid thus deprived of its heat will be reduced to 
a temperature below the freezing point and become ice. 

96. The diminution of temperature produced by the evaporation 
of ether is so considerable, that by means of it mercury may be 
reduced to the form of a solid. This maybe effected by inclosing , 
a small quantity of mercury in a flattened spheroid of thin glass, 
and covering it with thin muslin on which ether is to be dropped 
as fast as it evaporates, and the heat will thus be so rapidly ab- 
stracted from the mercury that it will soon be frozen to a solid 
mass. 

97. Water alone will boil speedily under the exhausted receiver 
of an air-pump, at the temperature of about 100 degrees of Fah- \ 
renheit; but in this case the ebullition soon ceases, in consequence ' 
of the pressure of the steam or aqueous vapour, which occupies 
the space from which the air has been withdrawn. 

98. The manner in which a liquid may be made to boil by dimi- 




■Io what manner may water be made to boil below 212°? 

What two contrary effects may be exhibited by withdrawing; atmos- 
pheric pressure from the surface of two liquids ? 

Explain tbe manner in which the experiment is to be conducted. 

What effect may be produced by dropping ether on a capsule filled 
with mercury ? 

At what temperature will water boil in the exhausted receiver of an 
air-pump ? 



310 



PYRONOMICS. 




nishing th? pressure of the atmosphere on its surface may be 
amusingly exhibited by means of the following experiment: 

Let a stop-cock be fitted into the neck of a Flo- 
rence flask, containing a small quantity of water, 
and after holding the flask over the flame of a spirit- 
lamp till the water boils and partly escapes in the 
form of steam through the stop-cock, let it be sud- 
denly removed from the flame, at the same time 
shutting the stop-cock; the ebullition will soon 
cease, and the flask is to be plunged into a jar of 
cold water, as represented in the margin. The 
water in the flask will instantly begin to boil again, 
inconsequence of the condensation of the included steam, and the 
vacuum thus formed in the upper part of the flask. If it be kept 
long immersed in the jar of water, the ebullition will cease from 
the gradual cooling of the water within the flask; but if it be 
taken out of the jar and held near the fire, fresh steam will be 
formed, and the ebullition may be renewed by plunging the flask 
afresh into the cold water. 

99. The mode of making liquids boil at a comparatively low 
temperature by the diminution of surface pressure, has been ad- 
vantageously adopted in some manufacturing processes. Thus it 
has been applied to practice in the art of refining sugar, the saccha- 
rine syrup being concentrated by this means to the point at which 
it crystallizes or granulates, without any hazard of its burning, 
or becoming decomposed by excess of heat. In the preparation 
of vegetable extracts for medical purposes, similar processes have 
been adopted ; and also in making jellies or other kinds of con- 
fectionary. 

100. Distillation is an operation conducted on similar principles 
with those just described ; but the object is different, for the vapour 
or steam which, in refining sugar, or making extracts, is dissipated 
and suffered to escape, as useless, is on the contrary, in distilla- 
tion carefully preserved, and reduced again to the liquid form by 
condensation. The method of distilling at a low temperature, 
by removing the pressure of the atmosphere, has been profitably 
employed in cases where it was a principal object to obtain pro- 
ducts as free as possible from an empyreumatic flavour, or peculiar 
disagreeable taste. Mr. Henry Tritton has invented an appara- 
tus for distilling spirits, by means of which the vapour is raised 
in a vessel not exposed as usual to the fire, but surrounded with 
hot water ; and the pipe proceeding from the upper part of it, after 



In what other manner may ebullition at low temperature be exhibited r 

How may it be repeated wben the liquid has become cold ? 

In what arts has advantage been taken of boiling- under diminished 
pressure ? 

How does distillation differ from the mere concentration of liquids? 

For what purposes is distillation at low temperatures chieflv import- 
ant J 

What is Use peculiarity of Tritton's distilling apparatus? 



I'APIX'S DIGESTER. 311 

passing in the usual way through a large body of cold water, ter- 
minates in a spacious cavity or close vessel, from which the air 
can be extracted by an air-pump or exhausting syringe. A similar 
process has been used with advantage in the distillation c.{' vinegar. 

101. As liquids boil readily at comparatively low temperatures 
when the pressure of air or elastic vapour on their surfaces is in- 
considerable, so they remain unevaporated at relatively high tem- 
peratures, if exposed to extraordinary compression, as when con- 
fined in a strong close vessel. Such an engine is that called Papin's 
Digester, from the name of the inventor. It consists of a metallic 
vessel of a cylindrical form, with very thick sides, having a cover 
fitting air-tight, and confined by a cross-bar fastened with screws. 
When such a vessel, partly filled with water, is exposed to the 
heat of a fire, a quantity of vapour will be formed within it, which 
being prevented from escaping will press powerfully on the sur- 
face of the liquid, and prevent ebullition, though the heat of the 
water be raised far above the boiling point, while the quantity and 
elasticity of the included vapour or steam will also be augmented. 
The digester ought to be furnished with a safety-valve, which may 
open when the steam acquires a certain degree of force, below the 
estimated pressure which the sides of the vessel would be capa- 
ble of withstanding, and thus the risk of its bursting if over-heated 
would be obviated. Such machines are employed for extracting 
the gelatinous matter from bones to make portable soup, and for 
other purposes. 

102. The temperature of steam is always the same with that of 
the liquid from which it is formed, while it remains in contact 
with that liquid ; and as the elastic force of the vapour is in- 
creased in proportion to its degree of heat, the amount of pressure 
which it exerts will depend on the temperature at which it is 
formed. Hence the distinction between high and low pressure 
steam and steam-engines. 

103. When steam begins to be produced, as in the process of 
making water boil, and the heat overcomes the atmospheric pres- 
sure on the surface, small bubbles are formed adhering slightly 
to the sides of the vessel, as may be conveniently observed by 
using a Florence flask or any other thin glass vessel. These bub- 
bles are formed most rapidly at those points against which the 
flame is most strongly directed ; and if any particular portion of 
the surface of a common boiler be more intensely heated than the 
surrounding parts, and the metal become uncovered by the liquid, 
when the water again comes in contact with it, very elastic steam 

Under what circumstances may liquids be made to undergo a high tem- 
perature without evaporating ? 

Describe Papin's digester. 

What relation exists between the temperature of vapour and that of 
the liquid from which it rises ? 

What distinction arises from the difference of temperatures at which 
it is produced ? 

In what manner Is the production of steam first manifested ? 

In what parts of a boiler will its developervent be most conspicuous ? 



312 



PYRONOMICS- 



will be suddenly formed, which may cause the boiler to burst. 
Such appears to be the most probable mode of accounting- for the 
numerous accidents resulting from the employment of steam as a 
moving power. 

104. Mr. Perkins has invented an improved steam-boiler, in 
which a constant circulation of the water is kept up, through a tube 
or open cylinder in the centre of the boiler, which sweeps off the 
bubbles from the heated surface of the vessel as fast as they are 
produced ; and thus the formation of steam goes on with uniform 
regularity. He had observed that two vessels being filled with 
water, and one placed wdthin the other, w r hen heat is applied so 
that it. can only reach the inner vessel through the liquid contained 
in the outer one, no steam-bubbles will rise in the former, while 
they will be rapidly formed in the latter. The fluid in the ex- 
terior vessel, consisting of water mixed with air-bubbles, and that 
in the interior vessel of Avater only, the contents of the two ves- 
sels at the same temperature will differ in specific gravity, those 
of the outer vessel of course being the lightest.. If therefore the 
bottom of the inner vessel be removed, so that it will constitute 
an open cylinder with its upper edge a little below the surface of 
the water in the larger vessel, and supported in that position, as 
shown in the annexed figure, the unequal density of the fluids in 
the exterior and interior parts of the 
boiler, when exposed to the action of fire, 
will cause the formation of a circulating 
current. 

105. The bubbles contained in the v 
water of the outer vessel, adjoining the 
fire, will rise continually to the surface; 
when at a low 7 temperature with a powder 
somewhat exceeding the difference be- 
tween the specific gravities of air and 
water, but if the heat be augmented, and 
the bubbles formed more rapidly, the 
difference of specific gravity cf the re- 
spective fluids will be increased, and 
also the velocity and force of the current. 
For the fluid in the inner vessel or cy- 
linder, being free from bubbles, will, in consequence of its supe- 
rior specific gravity^ descend and arrange itself beneath the rising 
Columns of the outer vessel, and thus continue the circulation. 

106. If the fire be urged so as to produce an extremely intense 
heat around a boiler of this construction, so rapid and forcible will 
be the ascending current, that it will draw into its vortex and 
carry upwards sand, gravel, or stones, or almost any kind of 




In what manner has Perkins sought to render the action of the surface 
of a boiler uniform ? 

Explain the manner in which the circulation is maintained by the pro- 
duction and escape of vapour ? 



THE STEAM-ENGINE. 313 

heavy substance of moderate size which may happen to be in 
the boiler, sweeping off, in its ascent, all the steam-bubbles which 
form on the interior surface of the boiler, and keeping it clear from 
the vapour which might otherwise interrupt the free passage of 
the heat which it receives into the water ; and by the uniform and 
constant agitation of the whole mass of the liquid, a regular and 
abundant absorption of heat takes places, and steam is evolved 
with astonishing rapidity. 

107. The steam-engine, a machine of the highest importance, 
the effective power of which depends on the expansive force of 
steam or vapour, its general construction and mode of action may 
here be described. The vapour of water occupies a space about 
1700 times larger than the bulk of the water from which it is 
formed ; and hence it may be conceived that in consequence of 
its expansibility it must strongly resist compression, and that the 
impetus thus obtained may be variously directed or modified so as 
to produce motion. 

108. At what period steam was first employed as a moving 
power is uncertain. However the mode of thus applying it, was 
known as early as the middle of the seventeenth century, since 
the Marquis of Worcester in his " Century of Inventions," pub- 
lished in the reign of Charles II., describes a machine for pro- 
ducing motion by the force of steam ; but though the idea of using 
steam as a moving power seems to have occurred to several persons 
about the same period, the invention of the steam-engine properly 
so called may be fairly ascribed to an ingenious man named New- 
comen, who was a locksmith in the West of England; and a 
patent for such a machine, for raising water from mines, was taken 
out bj' Newcomen, in conjunction with Captain Saver} 7- , an engi- 
neer, who probably contributed to the improvement of the inven- 
tion. 

109. The mode in which steam is made to act is by causing it to 
raise a solid piston working in a cylinder, like that of a forcing-pump 
or fire-engine ; and the piston-rod rising by the impulse of expand- 
ing steam admitted into the cylinder below it, must communicate 
motion to a beam or lever connected with it. W^hen the piston is 
thus raised, if the steam be suddenly condensed or withdrawn 
from under it, a vacuum will be formed, and the pressure of the 
atmosphere on the piston above will drive it down. It may then 
be raised afresh by the admission of more steam, to be condensed 
in its turn, and in this manner the alternate motion may be con- 

What striking effects are said to be produced by the currents between 
the two cylinders of Perkins's boiler ? 

What is the relation between the bulk of steam and that of the water 
from which it is produced ? 

How early was the force of steam, as a mechanical agent, probably ap- 
plied ? 

Who invented the steam-engine ? 

In what manner is the force of steam applied in that machine ? 

In what way did the atmospheric engine of Newcomen become effect- 
ive after the piston had been raised bv the steam ? 
2D 



314 PYRONOMICS. 

timied indefinitely. Newcomen's claim to be considered as an 
inventor depends on his having been apparently the first person 
who conceived the idea of condensing the steam the moment it 
had effected its object, by throwing into the cylinder a jet of cold 
water. 

110. Two very important improvements on the original engine 
were made by the celebrated James Watt. He observed that the 
cooling of the cylinder by the water admitted into it lessened the 
expansibility of the steam it received, and that thus much power 
was dissipated : to prevent which, he contrived a method of with- 
drawing the steam from the principal cylinder into another, in 
which the condensation takes place, and from which the water it 
yields is returned to the boiler to form fresh steam. The other 
improvement consisted in employing the expansive force of steam 
to depress the piston as well as to raise it. In the original, or 
atmospheric engine, the piston, as above stated, was driven down 
by the mere impulse of atmospheric pressure ; but in the improved, 
or double-action engine, steam is admitted into the cylinder above 
the raised piston at the same moment that it is removed below it; 
and thus the expansive force of steam is exerted in the returning 
as well as the ascending stroke, and a much greater impetus is 
given to the machinery than by the old method.* 

On what does his claim to the invention of the steam-engine rest ? 
In what did the two principal improvements of Watt consist ? 
How does his double-acting engine differ from Newcomen's, in regard 
to the effective mover ? 

* The following notices concerning the invention and improvement of 
the steam-engine are furnished by Dr. T. Young : — Denis Papin, in 1695, 
published an account of " a mode of employing the force of steam, by 
removing the fire continually from one part of the machine to another." 
Captain Savery exhibited a model of a steam-engine, June 16, 1699, 
which is described in the Philosophical Transactions. The date of Sa- 
very and Newcomen's patent for a steam-engine is in the year 1705 ; and 
the latter " introduced the piston." Among the improvers of this valu- 
able machine, Dr. Young mentions the names of De Moura, Smeaton, 
Beighton, Francois, who contrived " an engine without a piston, working 
the cocks by a tumbler ;" Droz, Cartwright, Hornblower, Woolf, and 
Edelcrantz, besides Watt. — Lectures on Natural Philosophy, 1807, vol. 
ii. pp. 257, 258. 



DESCRIPTION OF THE STEAM-ENGINE. 

PiSfflPPlSBI 



315 




111. The preceding figure will enable the reader to form a cor- 
rect idea of the principal parts of a steam-engine, and of its mode 
of action. AB denotes the principal cylinder; P its piston, act- 
ing by its rod Y on the extremity of the beam G H, the other ex- 
tremity of which is connected with the fly-wheel ; C, a tube or 
passage by which steam formed in the boiler is conveyed to the 
conducting pipes T U, to be admitted on either side of the piston 
P alternately; O, the fly-wheel, which by the rods R S, moving 
eccentrically, acts upon the rectangular lever V, which by means 
of the valve Z regulates the admission of steam by the conduct- 
Delineate separately the several parts of Watts's double-acting low 
pressure engine, and explain their uses. 

Make a drawing of the whole engine, and show the connexion of these 
parts. 



316 PYROXIMICS. 

ing pipes; M, the condenser; X, a tube by which the steam 
passes from the cylinder into the condenser ; N, a tube to convey 
the water after condensation to the pump L ; F, the piston of the 
pump L, worked by its rod E attached to the beam G H ; K the pis- 
ton-rod of a pump to inject water into the condenser. 

112. From this description, the mode of action of the engine 
may be readily understood. Suppose the piston P to be at the top 
of the cylinder A B, the lower part being filled with steam, then 
by means of the lever V, the steam-valve Z will be drawn down 
so as to admit steam by the upper branch of the conducting pipe U, 
into the cylinder above the piston : and at the same time a pas- 
sage will be opened to let the steam below escape into the con- 
denser. Thus the piston will be driven to the bottom of the cy- 
linder, when the steam-valve again opens to admit steam by the 
lower branch of the conducting pipe T, into the cylinder below 
the piston, while the other passage also opens to permit the steam 
above the piston to escape through the tube X into the condenser. 
Thus the manner in which the piston alternately rises and falls 
is shown, and by the connexion of its rod with the lever G H, it 
works the pumps, and turns the fly-wheel, whence the moving 
power may be propagated through trains of machinery for any 
purpose required. The fly-wheel may be moved in the manner 
represented in the figure, by a crank connected with a rod descend- 
ing from the arm H of the great lever ; or the toothed wheels 
called the sun and planet wheel may be applied, in the mode that 
has been explained elsewhere.* 

113. Various other arrangements are adopted for modifying or 
regulating the motions of different parts of the machine. Thus 
the piston rising vertically is connected by a system of jointed 
rods with the extremity of the arm G of the great lever; and as 
that lever turns on a pivot, the end of the arm must form an arc of a 
circle, but by means of the rods the motion is so modified that the 
piston is allowed to rise in a curve of double curvature of so large 
radii at the point described, as not to differ sensibly from a right 
line.f Another contrivance, regulating the velocity of a steam-en- 
gine, is that called the governor, previously described, which by the 
rising of the revolving balls closes, and by their descent opens the 
passage from the boiler to the cylinder;:}: and there are various 
others adapted to particular purposes. 

114. It has been mentioned that the degree of the elastic force 
of steam depends on the amount of pressure sustained by the sides 
of the vessel in which it is formed. In the common low-pressure 

By what two methods has the alternating motion of the piston rod been 
converted into continued rotary motion ? 

For what purpose is the system of jointed rods invented by Watt ap- 
plied to the steam-engine ? 

What is the elasticity of steam used in engines acting on the principle 
of Watt ? 

* See Treatise on Mechanics, No. 210 f Ibid. No. 220. 

\ Ibid. No. 228. 



HIGH-PRESSURE ENGINE. 317 

engine the steam used is generally formed under a pressure not 
exceeding twenty pounds on a square inch, and therefore when the 
expansive force of the steam exceeds it, the valve opens, and the 
force of the steam is consequently reduced. This pressure is only 
five pounds more than that of the atmosphere, and the boiler is fur- 
nished with a safety-valve, loaded with that weight to each square 
inch of its surface ; but in the double-action engine, the pressure 
of the atmosphere being excluded, the whole pressure of twenty 
pounds is by the aid of the condenser made available ; and thus 
such an engine, if its piston be of equal size, will have the same 
power as a high-pressure engine working with steam of the force 
of thirty-five pounds on the square inch, because fifteen pounds 
are here employed in overcoming the resistance of the atmosphere, 
into which the steam is finally thrown. 

115. The high-pressure engine, being simpler in construction, 
as well as smaller, than the double-action low-pressure engine, 
is more advantageously used than the latter, where it is requi- 
site to employ considerable .power within a confined space; 
and therefore it has been adopted in steam carriages. In these 
engines, the steam is not condensed, but is suffered to escape- 
after it has acted on the piston ; and as it is formed under extra- 
ordinary pressure, varying from fifty or sixty to two hundred and 
sixty pounds on the square inch,* its expansive force is relatively 
very great. The attention of those who have been engaged in 
the construction and improvement of steam-carriages has there- 
fore been chiefly directed to the contrivance of boilers in which 
high-pressure, steam may be formed with the least possible risk 
of explosion; and Mr. Goldsworthy Gurney and others appear to 
have so far succeeded as to have produced carriages worked by 
steam in which persons may travel at least as safely as in coaches 
drawn by horses, and with a degree of velocity incomparably 
greater. 

How much of the force of high steam is lost by the resistance of the 
air to its final expulsion from the cylinder ? 

What renders the high-pressure engine peculiarly adapted to locomo- 
tive carnages ? 

* See Gordon's Treatise upon Elemental Locomotion, 1832, pp. 62, 
80, 96, and 100. 

2d2 



318 



PYRONOMICS. 



Oliver Evans's Steam Engine. 




Oliver evans's steam engine. 319 

116. The high-pressure steam engine invented by Oliver Evans 
of Philadelphia, in 1784,* and for which he obtained a patent from 
the. state of Maryland in 1787, (the confederated states not having 
adopted a general system of patents,) is the original of all those 
powerful machines which for the last few years have astonished 
the world with their wonderful performances. 

117. The accompanying figure is a pretty accurate representa- 
tion of a model of Evans's engine, now in the collection of the 
Franklin Institute. By a comparison with the machine of Watt, 
it will be seen how greatly the genius of its inventor had simpli- 
fied the structure which has called forth such lofty encomiums 
from some of Watt's biographers. It must be remembered that 
the inventor was not insensible to the peculiar adaptation of his 
machine to the purposes of locomotion on land, but that this was 
one of the express objects of his patent. The parts of the high- 
pressure engine will be understood by a reference to the figure. 

118. A is the working cylinder, to which the steam, equal to 
several atmospheres in pressure, is admitted by the pipe o and 
the rotary valve v. 

B is the boiler of a cylindrical form, with a return flue placed 
below the centre of the outer shell, so as to be constantly covered 
with water when it stands about at the level of the line B. 

S is the smoke pipe springing from the interior flue, after the 
latter leaves the head of the boiler. 

119. G is the fire grate or furnace, from which the flame passes 
in the direction indicated by the arrow. 

P is the force pump, which draws water from a reservoir of hot 
water, R, placed above its own level. This water is kept hot by 
the steam which escapes from the cylinder A after it has perform- 
ed its office there. 

p is the pump rod connected with the moving beam above. 

V is the safety valve connected with the boiler and furnished 
with a graduated lever and weight to regulate the pressure. 

120. I is the working beam connected to an upright support by 
the two rods k k, to the oscillating triangle T, the pump rodp, the 
piston rod /, and the shackle-bar b, which last gives motion to the 
fly-wheel W. 

g is a toothed wheel, geared to another of the same diameter, 
which being connected with the two equal bevel wheels at e, com- 
municate motion to the rotary valve v. 

s is the escape pipe, by which the steam is conducted to*the 
tank or reservoir R. 

By what means is the flow of steam into the cylinder in Evans's engine 
allowed to take place ? 

How is the interior flue arranged in reference to the water line ? 

How is the hot water force pump arranged with relation to the reser- 
voir from which it is supplied ? 

What is the purpose of the two small bevel wheels seen in the figure ? 

* Evans began to build steam-engines on his plan in 1801, hut in 1794 
he had sent drawings and specifications to England, where they remained 
on the death of Mr. Sampson, by \\\\oxn they were carried out. — Ed. 



320 / PYROXOMICS. 

Propagation of Heat. 

, 121. When any considerable mass of matter, whether consist- 
ing of a single substance, as a body of water or atmospheric air, 
or of several substances mingled together, exhibits a uniformity 
of temperature, if another substance, either more or less heated 
than the general mass be added to it, the equilibrium of tempera- 
ture will be partially disturbed, for a time, and then restored ; the 
whole mass taking heat, from the substance added to it, if the 
latter be comparatively hotter than the mass, and giving out heat 
to it, if it be relatively cooler. Heat is thus propagated, or com- 
municated from one body to others, having a tendency to become 
generally diffused among bodies, and cause them all to exhibit 
the same degree of therrnometrical temperature. There are two 
modes in which the propagation of heat may take place ; namely, 
by conduction, and by radiation. 

122. Propagation of heat, by conduction, always takes place 
when any substance is brought into contact with another which is 
relatively colder. Hence it is that the temperature of the air in 
deep cellars and caves seems to be higher in winter than in summer. 
The degree of heat in such places is at both seasons nearly the 
same ; but the surface of the body in winter being colder than the 
air of a subterraneous cave, will attract the heat from it, and in the 
summer, on the contrary, the air will rob the body of its superior 
heat. It appears, from the experiments of MM. Bertholet, Pictet, 
and Biot, that heat is communicated more readily by a stroke or 
blow from a heated body than by simple contact.* 

123. The laws of the propagation of heat through bodies by 
conduction, may be deduced from the following experiment : sup- 

^•pose a bar of metal, two or three yards in length, to be placed in 
\ communication with a constant source of heat, and let ten holes 
v be bored in it at equal distances from each other, from one end to 
the other, and filled with mercury, thermometers being plunged 
into the fluid metal in all the holes ; then deducting the difference 
of the temperature of the air from that of the several thermome- 
ters, we obtain the temperature of the bar at 'so many relative dis- 
tances from the source of heat. These distances must necessarily 
constitute an arithmetical progression of numbers, and it will be 

What effects result when a mass of matter at one temperature is mixed 
with another mass at a different degree of heat? 

In how many modes does the propagation of heat take place? 

What is meant by the term conduction ? 

What effect has percussion produced by a hot body different from that of 
simple contact ? 

In what manner may the laws of the propagation of heat through bodies 
be estimated ? 

What progression will the diminutions of temperature follow when the 
points of the solid under examination are at distances from the source 
of heat forming an arithmetical series ? 

* Memoires d'Arcueil, t. ii. p. 447. 



COXDUCTORS OF HEAT. 321 

found that the aecrease of temperature will take place in a geo- 
metrical progression, forming a rapidly diminishing scale of num- 
bers. The rate of diminution of heat is indeed so rapid, that it 
would be impossible to raise the temperature of one end of a bar 
of iron two yards and a half in length, a single degree, by any 
heat applied to the other extremity ; for the heat requisite for that 
purpose would be greater than what was sufficient to melt the iron, 
as might be shown by calculation. 

124. Though heat has a tendency to spread by conduction 
through all bodies, yet some receive and give it out with much 
greater facility than others. Among solid substances the power 
of conducting heat varies very considerably. Metals in general 
conduct it more readily than wood, and the power of conduction 
is different in different metals. Hence the handle of a metal tea- 
pot or coffee-pot is commonly made of wood ; since if it was of 
metal, it would become too hot to be grasped with the hand, soon 
after the vessel was filled with boiling water. 

125. Dr. Ingenhousz ascertained the difference of conducting 
power among several metals, by dipping into melted bees-wax v 
cylindrical rods of various metals of the same dimensions, and 
when the equal coating of wax on all the rods was become solid 
by cooling, he plunged them to the same depth into heated oil, 
and from the difference of time required to melt the wax, in each 
case, he inferred the conducting power of the respective metals. 

It thus appeared that silver was the best conductor of heat, then 
gold, tin, copper, platina, steel, iron, and lead. So that the power 
of conduction in metals seems to be independent of their density, 
tenacity, or fusibility ; for the specific gravity of silver is inferior 
to that of gold or platina, yet its conducting power is greater ; 
while it has less tenacity than either of those metals; and it is not 
so readily fusible as tin or lead. 

126. Next to metals, precious stones, as the diamond, the topaz, 
and other dense earthy compounds, appear to be the readiest con- 
ductors of heat : then stony bodies, porcelain, and glass, and po- 
rous earthy compounds, such as brick and pottery. Wood con- 
ducts heat very imperfectly, whether in its usual state or in tha't 
of charcoal ; either of which may be held by the fingers very near 
the part which is burning and red hot. 

127. Animal and vegetable substances of a loose texture, as 
fur, wool, and cotton, are extremely indifferent conductors of heat. 
Hence their utility, either as natural or artificial clothing, in pre- 
serving the warmth of the body, in consequence of the obstruc- 
tion they present to the passage of heat through them. It is pro- 
How far might a bar of iron be heated by exposing one end only to the 

most intense heat ? 

Which class of solids comprises the best conductors of heat ? 

To what practical purpose is the low conducting power of wood appli- 
cable ? 

What order did Ingenhousz find among the metals in regard to conduct- 
ing power r 

What class of bodies hold the second place in conduction ? 




322 pyroxomics. 

bable, however, that in such cases the effect partly depends on 
the quantities of air contained in the interstices of such loose sub- 
stances ; since air is one of the very worst conductors of heat. 

128. Liquids conduct heat very slowly and imperfectly. If 
mercury be poured into a jar, and boiling water poured over it, the 
metallic fluid will receive heat but slowly from the water above 
it. A thermometer let down a few feet below the surface of a 
pond or of the sea, would, on being drawn up, indicate a lower 
temperature than that of the surface water ; for the latter, heated 
by the rays of the sun, would communicate by conduction little 
or no heat to the water below. Indeed it has been questioned 
whether water has the power of conveying heat at all by conduction. 
129. In the marginal figure, let A represent a cy- 
lindrical jar of w*ater, with an air thermometer, C, 
immersed in it, and having its bulb very near the 
surface; B is a small copper basin floating on the 
water just above the bulb, and separated from it 
only by a thin stratum of the aqueous fluid ; yet, 
when burning charcoal is placed in the basin, though 
the surface of the water beneath it may be heated to 
the boiling point, the temperature just below will 
scarcely be sufficient to produce any effect on the 
thermometer : so that it may be concluded that water does not 
transmit heat downwards by conduction. 

130. It may be reasonably inquired how it happens that water is 
readily made to boil by the application of heat. A little consid- 
eration will show that the effect in a great measure depends on 
the manner in which the liquid is heated, by placing it above the 
source of heat. Thus, the lower stratum of the liquid, being expand- 
ed by the heat communicated to it through the bottom of the con- 
taining vessel, rises to the top in consequence of its inferiority of 
specific gravity, and the water above sinks down to supply its 
place and be heated in the same manner, till .the whole mass ac- 
quires the same temperature. The mode in which ebullition is 
facilitated by the formation of air-bubbles, and the ensuing circu- 
lation of the fluid in ascending and descending currents, has been 
already described. 

131. Air, like water, appears to have no observable effect on the 
propagation of heat by conduction ; and it may be concluded that 
gaseous fluids conduct heat, if at all, with degrees of difficulty in- 
creasing in proportion to their rarefaction. It is owing to the ex- 
treme rarefaction of the atmosphere at great distances from the 
common level of the earth's surface, as upon high mountains, and 

On what circumstance do porous, animal and vegetable substances pro- 
bably depend for their low conducting power ? 

What facts and experiments show the low conducting power of liquids? 

Explain the apparatus by which this principle is illustrated. 

How does it appear that the rapid communication of heat to water is 
consistent with its low conducting power ? 

In what manner do gaseous bodies communicate heat ? 



THE CALORIC ENGINE. 323 

its increased capacity for heat, that the excessive cold observable 
in such situations is to be attributed. Yet though the atmosphere 
is so bad a conductor of heat, substances may be warmed or cooled 
by the relative temperature of the air ; for the expansion of air by 
heat, and necessary production of aerial currents, causes a rapid 
transmission of heat through the air, and thus the temperature of 
any body in contact with it may be raised or lowered according to 
circumstances. Air also readily conveys heat by radiation, as will 
be subsequently explained. 



The Caloric Engine. 

132. The principle of communicating heat by circulation, is ap- 
plied in connexion with the rapid absorption and subsequent com- 
munication of heat by metallic bodies, in the construction of a 
machine which has recently been invented by Mr. Ericson, of 
London. It is called the Caloric Engine, and is actuated by the 
successive dilatation and contraction of a quantity of compressed 
and partially heated atmospheric air, or other permanent gas. 

133. This air or gas being made to circulate in opposite cur- 
rents through a series of small metallic tubes, causes a constant 
transfer of heat from one part of the machine to another, whereby 
an alternate dilatation and contraction of the impelling medium is 
effected and kept up. 

134. Thus the Caloric Engine possesses a novel and important 
feature when compared with the steam-engine, viz., that of being 
actuated over and over again by the same heat, or nearly so ; and 
it may be added, that it presents to natural philosophy an illustra- 
tion of the fact that heat does not lose its energy in producing me- 
chanical force, but remains in undiminished quantity after having 
caused the dilatation which produces that force. At the same time 
this new invention presents to mechanical science a wide field for 
improvement, since (unlike the steam-engine) its principle is such 
that the quantity of force it produces has no other relation or pro- 
portion to the fuel it requires than that established by a more or 
less perfect machine and transferring apparatus. 

135. The action of the Caloric Engine and the transfer of the heat 
will be ready understood by referring to the annexed diagram. 

On what principle is Ericson's caloric engine constructed ? 
What essential feature does it possess different from that of the steam- 
en srine ? 



324 



PYRONOMICS, 




136. The engine consists of two cylinders, A and B, of unequal 
diameters, the large one being always kept at a high temperature, 
and the small one always cool. These cylinders are provided with 
pistons and valves, similar to those of a high-pressure steam-en- 
gine, and their piston-rods are connected so that the one piston 
cannot move without the other. The two cylinders communicate 
with each other by means of a number of small tubes, C, passing 
through a vessel, D, called the regenerator, and all terminating in 
chambers or caps, E and F, attached to the ends of the regenerator, 
and so arranged that the hot air, after having performed its duty in 



In what state is the larger cylinder of Ericson kept ? 

Exulain the several parts of this machine, and state their several uses. 



THE CALORIC ENGINE. 325 

the large or working cylinder A, passes through the pipe G, into 
the body of the regenerator D, for the purpose of giving out its heat 
to the small tubes C, in its passage towards the small cylinder B, 
and thereby becomes cooled and reduced in volume. 

137. In order to effect this more completely, a number of parti- 
tions, H, having segments cut out alternately from their tops and 
bottoms, are introduced into the body of the regenerator, giving a 
very circuitous motion to the hot air in its passage from the pipe 
G to the pipe K. 

The cold air, forced, by the action of the piston of the small 
cylinder in a contrary direction, through the small lubes (these 
being also provided with small partitions for changing or intermix- 
ing the particles of air), will, during its passage from the cap F 
to the cap E, on its way to the hot cylinder, take up the heat im- 
parted to those tubes by the contrary hot current which passes 
through the body of the regenerator, and thereby become heated 
and enlarged in volume. 

138. It will be evident that if compressed air be admitted into 
both cylinders on one side only of their pistons, the greater sur- 
face of the one will be acted upon with greater force than the less 
surface of the other; hence motion must ensue : and by reversing 
the position or the " slide valves" at the termination of each stroke, 
it will be continued. It need hardly be stated that the difference 
of the volumes of air contained in the two cylinders will cause 
neither deficiency nor accumulation during the action ; because in the 
large cylinder the air is in a heated state, and in the small one cold. 

139. Some loss of heat will of course be unavoidable in the 
transferring process, and this is compensated by passing the air, 
previous to its entering the hot cylinder, through a series of small 
tubes, L, communicating with the cap E, and induction-pipe Q, 
and exposed to fire, contained in a stove, M, the combustion being 
supported by ordinary draught, and the waste heat made to pass 
round the regenerator, and carried off at N into a common chim- 
ney. At the same time the air which has passed through the body 
of the regenerator still retains a small quantity of heat when en- 
tering the pipe K ; it is therefore passed through tubes O, immersed 
in cold water, or exposed to some other cooling medium, previous 
to entering the small cylinder. 

140. The marked difference, then, between the caloric engine 
and the steam-engine consists in this : that the heat, which is re- 
quired to give motion to the caloric engine at the commencement, 
is returned by the transferring process, and thereby made to work 
the engine over and over again, requiring but a small addition of 
heat to compensate for losses caused by radiation, &c. ; while on 

What is the purpose of the small perforated partitions in the regene- 
rator, and in its included tubes ? 

To what cause of loss is the air in this engine exposed ? 

Mow is that loss supplied ? 

How is the quantity of disposable force in this engine proportioned to 
the size of the two cylinders respectively? 
'2E 



326 PYRONOMICS. 

the other hand, in the steam-engine the heat is constantly lost by 
being thrown either into a cold condenser, or into the atmosphere, 
like so much waste fuel. 

141. From what has been stated it must be inferred that those 
bodies which absorb heat most freely also part with it most rapidly ; 
that is, they are sooner heated and more speedily become cooled 
than other bodies. Metals, which are generally the best conduc- 
tors, and therefore communicate heat soonest, cannot be handled 
when raised to a temperature of more than 120 deg. ; water be- 
comes scalding hot at 150 deg. ; but air applied to the skin occa- 
sions no very painful sensation when its heat is far beyond that 
of boiling water. 

142. Some curious experiments on the power of the human body 
to withstand the influence of heated air were made by Sir Joseph 
Banks, Sir Charles Blagden, Dr. Solander, and Dr. George For- 
dyce ; and an account of them was published in the Philosophical 
Transactions for 1775. These gentlemen found that they could 
remain for some time without inconvenience in a room where the 
heat was 52 deg. above the boiling point. But though they could 
thus bear the contact of th'e heated air, they could not bear to 
touch any metallic substance, as their watch-chains or money. 
Eggs placed on a tin frame in the heated room were roasted hard 
in twenty minutes ; and a beef-steak was overdone in thirty-three 
minutes. Similar experiments have been often repeated, especially 
by persons who have made public exhibitions of their power of 
sustaining heat, in which, however, there is nothing extraordinary, 
or which may not be explained as the result of habitual practice. 

143. Mr. Chantrey, the celebrated sculptor, made some obser- 
vations analogous to those just noticed, by means of a stove or 
oven which he uses for drying plaster casts and moulds. A ther- 
mometer suspended in this heated cell, usually stands at 300 deg. 
yet the workmen enter and remain in it occasionally some minutes, 
without difficulty. Persons unused to such a temperature found 
that they could easily support the heat for a short time ; but one 
gentleman inadvertentlj 7- entering the oven with a pair of silver 
mounted spectacles on, had his face burnt where the metal came in 
contact with the skin ; thus experimentally ascertaining the dif- 
ferent effect of air and silver at the same temperature. 

144. On the strong attraction of metals for heat, and the conse- 
quent facility with which they abstract it from other bodies, de- 
pends, in a great measure, the effect of Sir Humphry Davy's 
safety-lamp, to be used in mines, or other places infested with that 
kind of inflammable gas called fire-damp. Flame is gas, oi air 

What relation exists between the power of bodies to absorb and tc 
communicate beat ? 

How is the difference of various substances in this particular strikinglj 
exhibited ? 

Describe the experiments of Banks, Blagden, and others. 

What curious observations were made by Chantrey ? 

On what principle is the usefulness of Davy's safety-lamp dependent ? 



' RADIATION OF HEAT. 327 

m the state of combustion, and all gases require a very high tem- 
perature to make them burn ; so that the flame of gas becomes 
extinguished by lowering its temperature. This may be experi- 
mentally demonstrated by approaching to a weak flame a large 
mass of iron, as by gradually lowering a thick iron ring over the 
flame of a small cotton thread dipped in oil ; which, being deprived 
of its heat by the metal, would go out. 

1 15. In a similar manner, the temperature of any inflammable 
vapour may be reduced below what may be termed the burning 
point, by passing through fine wire-gauze. Thus, if a small por- 
tion of camphor be placed in the centre of a piece of wire-gauze 
about a foot square, and a lighted candle applied to the under sur- 
face, the vapour of the camphor will be kindled and burn below 
the gauze, without passing through to inflame the camphor upon 
it. Hence may readily be understood the effect of the safety-lamp, 
which is a kind of lantern of fine wire-gauze, within which a candle 
or wick, fed with oil, will burn in security amidst an atmosphere 
of fire-damp ; for though the vapour may enter and become inflamed 
within the lantern, the flame cannot pass through the close tissue 
of the wire-gauze to occasion an external explosion. 

146. Heat is not only communicated from one body to another 
by conduction, or by means of circulating currents, but it is also 
conveyed to considerable distances, through any elastic fluid, as 
air, by radiation. This mode of the transmission of heat resembles 
that in which light is propagated ;. and, as light and heat are fre- 
quently transmitted together by radiation, the effects of radiant 
heat were generally attributed to the light by which it is observed 
to be accompanied. The ancient Greeks and Romans were ac- 
quainted with some of the extraordinary effects of radiant heat 
produced by burning-glasses ; and thus Archimedes is said to have 
consumed the ships of the Romans by such instruments, during 
the siege of Syracuse ; and several centuries later the philosopher 
Proclus in the same manner destroyed the fleet of Vitalianus, 
before Constantinople. 

147. Many experiments have been made in modern times on the 
effect of the transmission of radiant heat through convex lenses, 
and of its reflection from concave mirrors, which show that by 
these means its power may be vastly augmented, and which tend, 
upon the whole, to corroborate the statements of ancient writers 
relative to the action of burning-glasses. 

148. The following results are said to have been obtained from 
the exposure of different substances to the rays of the sun, col- 

"VVhat is the true nature of flame ? 

How can we prove that flame is prevented from traversing wire-gauze 
by the cooling- of the horning gas ? 

What other substances besides permanent inflammable gases, may be 
kept below the burning point, by wire-gauze. 



Explain the difference between radiation and conduction. 
What evidence have we that the ancients knew the effect of radial 
What results have been obtained by modern experiments on bur 
lenses ? 



iation ? 
ning 



328 PYRONOMICS. 

lected by means of a lens two feet in diameter, with a focal dis- 
tance of three ells, in experiments made at Leipsic in 1G91. 

149. Pieces of lead and tin were instantly melted ; a plate of 
iron was soon rendered red hot, and afterwards fused ; a burnt 
brick was converted into yellow glass; and amianthus, one of the 
most refractory bodies, was in a short time reduced to the state of 
black glass.* Analogous experiments were subsequently per- 
formed in France, with a more powerful lens, constructed by order 
of M. Trudaine de Montigny ; and in England, with Parker's 
burning- lens, which was presented to the Emperor of China, when 
Lord Macartney was sent on an embassy to the court of Pekin. 
This last instrument was a double convex lens, three feet in di- 
ameter, three inches thick in the centre, and weighing 212 pounds. 
Its aperture, when set, was 32^ inches ; its focal distance G feet 
8 inches : but the focal length was generally shortened by a smaller 
lens. The most refractory substance fused was a cornelian, which 
required 75 seconds for its fusion ; a chrystal pebble was fused in 
6 seconds ; and a piece of white agate in 30 seconds. f 

150. Important experiments have likewise been made with con- 
cave mirrors and with combinations of plane mirrors, which, 
though relatively less powerful than lenses, may more conveniently 
be rendered efficient at greater distances. M. Dufay used both 
parabolical and spherical mirrors made of plaster of Paris, gilt 
and burnished ; and with one of the latter, 20 inches in diameter, 
he set fire to tinder at the distance of 50 feet. The Abbe Nollet 
made corresponding experiments with concave mirrors constructed 
of pasteboard, covered with silver or gold leaf and burnished.}: 
But the most remarkable experiments of this nature were those of 
BufTon, who had a machine composed of one hundred and sixty- 
eight small plane mirrors, so arranged that they all reflected ra- 
diant heat to the same focus. By means of this combination of 
reflecting surfaces he was able to set wood on fire at the distance 
of 209 feet, to melt lead at 100 feet, and silver at 50 feet.§ 

151. The heat of the sun may be concentrated by means of a 
concave mirror, or by being transmitted through a convex lens ; 
but the heat of burning bodies in general, though readily reflected 
by a concave mirror of metal, produces little or no effect by means 

What remarkable effects were obtained by the Leipsic experimenters? 
What refractory materials were fused by Parker's lens ? 
What kind of reflectors were used by Dufay for burning mirrors ? 
What apparatus was employed by Nollet and BufTon for the same pur- 
pose ? 

How may the heat of the sun be concentrated ? 

How is common culinary heat affected by transparent solid lenses? 

* Sigaud de la Fond Elem. de Physique, vol. iv. pp. 172, 173. 

•\ Dr. Young, in Lect. on Nat. Philos., vol. ii. p. 407, from Cavallo. 

| V. Histoire de l'Academie Roy. des Sciences, An. 1726, p. 165. Nol- 
let Lecons de Physique, t. v. p. 218. 

§ V. Hist, de f'Academie Rov. des Scien., An. 1747, p. 82; and 1748, 
p. 305. 



RADIATION OF HEAT. 



329 



of a lens. In a paper published in the Memoirs of the Academy 
of Sciences of Paris, in 1682, by M. Mariotte,he stated that radiant 
heat from a common fire, concentrated by a concave mirror, has 
its effect destroyed by the interposition of a plate of glass ; and 
the Swedish philosopher, Scheele, from numerous experiments, 
inferred that glass intercepts entirely the radiant heat of a fire ; 
and that a glass mirror reflects the light, but prevents the passage 
Df the heat, while a metallic mirror reflects both heat and light. 
It has however been since discovered, that though the heat of burn- 
ing bodies commonly exhibits different effects, in passing through 
glass, from those which are perceived in the passage of solar heat, 
they may probably depend on the far inferior intensity of the heat 
arising from combustion compared with that of the sun. For 
when a very intense artificial heat with light is produced, as that 
of charcoal ignited by a voltaic battery, if a small lens be placed 
before the brilliant star of fire thus obtained, and its focus be cast 
on the ball of a delicate air thermometer, some elevation of tem- 
perature may be perceived. 




152. That heat radiates from bodies in right lines, and that it 
may be reflected to a focal point by a mirror, like light, may be de- 
monstrated by the apparatus represented above. It consists of 
two concave mirrors, A and B, of planished tin or plated copper, 
about one foot in diameter, and placed exactly opposite each other, 
at the distance of about ten feet. In the focus of one mirror, at C, 
must be placed a heated body, as a ball of iron; and in the focus 
of the other mirror, at D, a differential thermometer. The rays of 
heat, then, impinging on the mirror A, are reflected through the air to 
the mirror B, whence they converge to its focus at D, and produce 
an effect on the thermometer proportioned to the degree of heat 
of the iron ball or other heated body. 

What result was alleged to have been obtained in regard to this sub- 
ject by M. Mariotte and by Scheele ? 

What is now found to be the fact in regard to the passage of the heat, 
produced by combustion, through glass ? 

What explanation is to be given of the difference between that and solar 
heat ? Describe the apparatus called Pictefs conjunctive mirrors. 

How does it appear that the effect on the thermometer is not the con- 
sequence of direct radiation? 



330 PYROXOMICS. 

153. That this effect is not produced by the mere dispersion of 
the heat through the air may be evinced by holding a pasteboard 
screen between the mirror B and the thermometer, when the latter, 
though as near the source of heat as before, would be hardly, or 
not at all, affected by it. And if the ball be moved out of the focus 
of the mirror A, towards the thermometer, though thus brought 
nearer to it, the effect will be greatly diminished. 

154. The flame of a candle, or a flask of boiling water, being 
substituted for the heated ball, the same effect will be produced. 
If a body yielding a stronger heat, as burning charcoal, or a red 
hot ball of iron, be placed in the focus of one mirror, and a piece 
of phosphorus in that of the other, the phosphorus will be instantly 
inflamed ; and in the same manner may be effected the detonation 
of fulminating silver, or the deflagration of gunpowder. For the 
exhibition of the latter experiments may be adopted by Sir H. Da- 
vjr's arrangement of the mirrors, vertically opposite to each other. 

155. An extraordinary and somewhat problematical phenome- 
non which may be exhibited by such mirrors, is the apparent 
radiation of cold. For if a ball of ice or snow be substituted for 
the heated iron in the focus of the mirror A, the thermometer will 
show a reduction of temperature. It has been hence inferred by 
some, that cold is a peculiar kind of subtile fluid, capable of being 
propagated by radiation ; but the effect has been more generally 
attributed to the abstraction of heat from the thermometer by the 
frozen mass opposite to it. 

156. Those bodies which reflect heat most powerfully, like the 
polished mirrors above described, do not acquire heat from the 
rays impinging on their surfaces ; so that such a mirror might be 
held a long time opposite to a fire without becoming perceptibly 
warmer. But if the surface of the metal be made rough by 
scratching it with sand-paper, or covered with paste mixed with 
chalk or lamp-black, it will rapidly absorb the rays of heat, instead 
of reflecting them. Hence it appears that the effect of radiant 
heat greatly depends on the state of the surfaces of bodies. 

157. " Leslie discovered, by experiments made in 1802, that the 
heat emitted by radiation was affected by the nature of the sur- 
face exposed. The action of a blackened surface of tin being 
100, that of a steel plate was 15, of clean tin 12, of tin scraped 
bright 16, when scraped with the edge of a fine file in one direction 
26, when scraped again across about 13, a surface of clean lead 19, 
covered with a gray crust 45, a thin coat of isinglass 80, resin 96, 
writing-paper 98, ice 85. Heat as well as light is so projected 
from a surface, as to be equally dense in all directions, conse- 

What cases of incipient combustion may be produced by reflected heat ? 

How is the apparent radiation of cold exhibited ? and how explained ? 

What relation appears to subsist between the reflecting and the absorb- 
ing power of bodies ? 

What is the effect of roughening or colouring the surface of a reflec- 
tor f 

What discovery did Leslie make in regard to the radiating power of 
different surfaces ? 



RADIATING SURFACES. 331 

quently from each point, in a quantity which is as the sine of the 
angle of inclination. The radiation is not affected by the quality 
of the gas in contact with the surface, but it is not transmitted by 
water."* 

158. As polished metals absorb heat very slowly, so heat is 
but slowly emitted from the surfaces of such metals ; and thus 
boiling .water would continue at a high temperature much longer 
in a silver tea-pot than in one of black earthenware ; so that ves- 
sels of polished metal are best adapted for preparing tea or other 
vegetable infusions. 

159. Substances of a light and very brilliant colour reflect heat 
readily, but do not absorb it ; while black or very dark coloured 
bodies absorb the heat that falls on them, reflecting little or none 
of it. If pieces of white cloth and other pieces of black cloth 
be laid, in similar circumstances, on the surface of snow, it would 
soon become melted beneath the black cloth, but remain perfectly 
solid under the white. In some of the mountainous parts of Eu- 
rope, the farmers are accustomed to spread black earth or soot 
over the snow, in the spring, to hasten its dissolution, and enable 
them to anticipate the period of tillage. 

1G0. It may be generally assumed that all bodies of unequal 
temperature tend to become of equal temperature ; if in contact, 
by conduction ; if at sensible distances, by radiation of the excess 
of heat; and in the latter case whether the radiation reach the 
cooler body directly, or by an intervening reflection.! 

What class of surfaces emit or radiate heat most readily ? 

What influence has colour on the absorbing and reflecting- powers of 
bodies respectively ? 

What advantage is taken in Europe of Franklin's discovery respecting 
the melting of snow beneath black surfaces ? 

In what two modes do all bodies of unequal temperatures tend to an 
equality in this respect? 

* Dr. Young's Lectures on Natural Philosophy, vol. ii. p. 407. 

t See Report on the present State of our Knowledge of the Science 
of Radiant Heat, presented to the British Association, by Professor Pow- 
ell, in 1832. 



332 PYRONOMICS. 



Works of reference on the subject of Pyronomlcs. 

The following, among other works on the science of heat, may 
be consulted in further prosecuting the study of this department. 

Thompson's Treatise on Heat and Electricity. 

Library of Useful Knowledge, treatise on Heat. 

" " " " on the Construction of 

Thermometers and Pyrometers. Two numbers. 

Webster's edition of Brande's Manual. Boston. 

Turner's Chemistry, by Dr. Bache. Phila. edition. 

Ure's Dictionary of Chemistry. Article Caloric. 

Leslie on Heat and Moisture. - 

Crawford on Animal Heat. 

Dalton's New System of Chemical Philosophy. 

Leslie's Experimental Inquiry into the Nature of Heat. 

Walker on Cold. 

Many articles in Silliman's Journal, the Journal of the Franklin 
Institute, Annales de Chimie, and other contemporary periodicals. 



OPTICS. 

1. Among the grand sources of our knowledge of the works of 
nature is the faculty or sense of sight or vision, to which we owe 
the perception of light and colours, and the means of judging 
concerning the forms and appearances of the numerous bodies 
around us. The highly curious, interesting, and important phe- 
nomena with w T hich we thus become acquainted constitute the 
subjects of the science of Optics,* or the theory of light and vision. 

2. This department of natural philosophy may be considered as 
furnishing topics for investigation under different points of view : 
1. As relating to the general properties of light, and its effect on 
the organ of vision ; 2. With reference to the reflection of light 
from the surfaces of bodies; 3. With reference to the refraction 
of light, or the alteration it undergoes in passing through transpa- 
rent bodies ; 4. As regards the phenomena of colours; 5. As re- 
spects certain modifications of reflected and refracted light, which 
have been characterized as resulting from the polarization of light. 

3. Among the multitudes of bodies which we can perceive, 
some are visible by their own light, and these are styled luminous 
bodies ; while others have no such illuminating property, and can 
be seen only by means of the light afforded by the former. Lu- 
minous bodies consist of those which are original and permanent 
sources of light, as the sun, fixed stars, and probably comets ; and 
those which exhibit light only under certain circumstances, es- 
pecially while undergoing combustion, as in the case of minute 
fragments of steel struck off by the collision of flint with steel, or 
in the common process of burning a candle, oil in a lamp, or coal- 
gas. 

4. Any bodies which do not interrupt the passage of light, or 
which admit of other bodies being seen through them, are called 
transparent bodies ;| those which prevent entiiely the passage of 
light are termed opaque bodies ; and those which allow other bodies 
to be seen through them obscurely and imperfectly are named semi- 
transparent substances. Transparency and opacity, however, de- 
pend much on the relative thickness or thinness of substances ; for 
even air, which affords less interruption to the passage of light 

What classes of phenomena are embraced in the science of optics ? 

Under how many and what different views may this science be regarded? 

On what is the distinction of luminous and non-luminous bodies founded ? 

How are the terms transparent, semi-transparent, and opaque respec- 
tively applied ? 

Are transparency and opacity to be regarded as absolute or relative 
properties of matter ? 

* From the Greek o^-rcuxt, to see. 

t The words transparent and diaphanous are synonymous ; the former 
being derived from the Latin, trans, through or beyond, and parens, ap- 
parent; and the latter from the Greek-, "&» *<?«,•>],•, shining through, or 
translucent. 

333 



334 optics. 

than any other land of matter, is not perfectly diaphanous ; nor 
will the densest metal completely prevent the influence of light. 

5. It has been calculated that the atmosphere, when the rays 
of the sun pass perpendicularly through it, interrupts from one 1-5 
to i of their light ; but when the sun is near the horizon, and the 
mass of air through which the solar rays pass is consequently 
vastly increased in thickness,- only 1-212 part of their light can 
reach the surface of the earth. "By a peculiar application of my 
photometer," says Sir John Leslie, "I have found that half of the 
incident light, which might pass through afield of air of the ordi- 
nary density, and 15^ miles extent, would penetrate only to the 
depth of 15 feet in the clearest sea-water, which is therefore about 
5400 times less diaphanous than the ordinary atmospheric medium. 
But water of shallow lakes, although not apparently turbid, be- 
trays a greater opacity, insomuch that the perpendicular light is 
reduced one-half in descending only through the space of six, or 
even two feet. 

6. The same measure of absorption would take place in the 
passage of light through the thickness of two or three inches of 
the finest glass, which is consequently 500,000 times more opaque 
than an equal bulk of air, or three hundred times more opaque 
than an equal weight or miosis of this fluid. But even gold is dia- 
phanous. If a leaf of that metal, either pure or with only 1-80 
part of alloy, and therefore of a fine yellow lustre, but scarcely 
exceeding 1-300,000 of an inch in thickness, and inclosed between 
two thin plates of mica, be held immediately before the eye, and 
opposite to a window, it will transmit a soft green light, like the 
colour of the water of the sea, or of a clear lake of moderate 
depth. This glaucous tint is easily distinguished from the mere 
white light which passes through any visible holes or torn parts 
of the leaf. It is indeed the very colour which gold itself assumes, 
when poured liquid from the melting-pot. 

7. A leaf of pale gold, or gold alloyed with about 1-80 part of 
silver, transmits an azure colour; from which we may, with great 
probability infer, that if silver could be reduced to a sufficient de- 
gree of thinness, it would discharge a purple light. These noble 
metals, therefore, act upon white light exactly like air or water, 
absorbing the red and orange rays which enter into its composition, 
but suffering the conjoined green and blue rays to effect their pas- 

What portion of the sun's light, when vertical, is supposed to reach the 
earlfi ? 

How great a portion is interrupted when the sun is near the horizon } 

What calculation has Leslie instituted between the transparency of air 
and that of water ? 

What is found to be the degree of opacity in shallow lakes compared 
With sea- water ? 

How much does the opacity of the best glass, weight for weight, exceed 
that of common air ? What examples of transparency are found in bodies 
commonly reckoned opaque ? 

How is the colour of light found to vary when transmitted through bo- 
dies which are imperfectly transparent? 



SOURCES OF LIGHT. 335 

sage. If the yellow leaf were to transmit only 1-10 part of the 
whole in ;ident light, we should only conclude, that pure gold is 
250,000 limes less diaphanous than pellucid glass. 

8. The inferior ductility of the other metals will not allow that 
extreme lamination, which would he requisite, in ordinary cases, 
to show the transmission of light. . But their diaphanous quality 
may be inferred, from the peculiar lints with which they affect the 
transmitted rays when they form the alloy of gold. Other sub 
stances which are commonly reckoned opaque, yet permit in vari 
ous proportions the passage of light. The window of a small 
apartment heing closed by a deal board, if a person within shut 
his eyes for a few minutes, to render them more sensible, he will, 
on opening them again, easily discern a faint glimmer through the 
window. If this board be planed thinner, more light will succes- 
sively penetrate, till the furniture of the room becomes visible, 
and perhaps a large print may he distinctly read. 

9. Writing-paper transmits about the third part of the whole in- 
cident light, and when oiled it often supplies the place of glass in 
the common work-shops. The addition of oil does not, however, 
materially augment the diaphanous qualit}?- of the paper, but ren- 
ders its internal structure more regular, and more assimilated to 
that of a liquid. The rays of light travel without much obstruction 
across several folds of paper, and even escape copiously through 
naste-board."* 

10. The chief sources of light, as already observed, are perma- 
nently luminous bodies, or celestial fire, especially the sun; and 
.errestrial fire, or that given out during combustion, or incandes- 
cence. There are, however, some cases in which light is exhibited 
under circumstances apparently unconnected with the influence of 
the solar rays, or of terrestrial fire. The exhibition of light ac- 
companies many electrical phenomena; as lightning, the luminous 
traits produced by brushing with the hand a cat's back in the dark, 
and many others which will be more particularly noticed in the 
subsequent part of this volume. 

11. Phosphorescence is another kind of luminous exhibition, 
where light is emitted without sensible heat, and the effect seems 
to be but remotely, if at all, dependent on either cf the grand 
sources of luminosity which have been pointed out. Common 

What relation may be computed to subsist between the transparency 
of gold and that of glass ? 

What would l>e the comparative transparency of gold and common air? 

I low may the partial transparency of wood be demonstrated ? 

What is the effect of oiling paper on its power of transmitting light? 

What are the chief sources of light? 

From what sources, independent of these, are the phenomena of light 
occasionally produced ? 

What is the distinction between phosphorescence and the luminous- 
ness of burning bodies ? 

* Leslie's Elements of Natural Philosophy, vol. i. pp. 'JO — 22. 



336 optics. 

phosphorus* is a highly combustible body, burning fiercely at a 
certain temperature, with intense light and heat. : it also gives out 
light at a very low temperature, without apparent heat, but this is 
the effect of slow combustion : it was, however, ascertained by 
Dr. Van Marum, a Dutch philosopher, that phosphorus covered 
^with dry loose cotton, or sprinkled with resin, would shine under 
the exhausted receiver of an air-pump, f a situation in which it 
seems impossible that any combustion can take place,, on account 
of the deficiency of atmospheric air. But there are phosphores- 
cent bodies which yield light under circumstances which have no 
connexion whatever with the process of combustion. 

12. Decayed wood, and sometimes peat or turf, have been ob- 
served to shine in the dark ; and some kinds of fish, as soles, 
whiting, tench, and carp become luminous when tainted, but 
before they grow putrid ; lobsters and crabs often display phospho- 
rescence in similar circumstances ; and also butchers' meat, occa- 
sionally. 

13. There are many animals of the lower orders that emit light 
in greater or less abundance while living. Among insects, the 
glow-worm (Lampyrus Spkndldula) is the most generally noted for 
its illuminating powers, in European countries, and the common fire- 
fly of the United States; there are, however, other insects in some 
degree possessing similar properties, as the common centipede, 
found under tiles or flowerpots in gardens, which when irritated 
gives out bright flashes of light. But the most remarkable shining 
insects are natives of the West Indies and South America; and of 
these the Elatcr Nbctilucus, a coleopterous^: insect, affords a splen- 
did specimen. " It is an inch long, and about one-third of an inch 
broad, gives out its principal light from two eye-like tubercles 
placed upon the thorax; and the light emitted from them is so 
considerable that the smallest print, may be read by moving one 
of these insects along the lines. "§ 

11. The surface of the sea is observed by the mariners to be 
occasionally illuminated ; and the light generally, if not always, 
is produced by certain marine phosphorescent animals. There are 
some peculiarities in these luminous appearances, which have been 
described as exhibiting five varieties ; " the first shows itself in 



How did Van Marum exhibit the phenomena of phosphorescence ? 

What examples of a purely phosphorescent appearance can be men- 
tioned ? 

How does it appear that neither combustion nor putrescence is neces- 
sary to the production of phosphorescence in animal substances ? 

Among what tribes of animals are the phosphorescent, classes cbiefly 
found ? 

* From jsojc, light, and -;£=.■, to bear. 

t See Arcana of Science, for 1832, p. 130 ; and Brewster's Edinburgh 
Journal of Science, X. S. 

£ So called from the character of the wings. 

4 Introduction to Entomology. By Rev. W. Kirby and W. Spence. 
8vo. vol. ii. p. 413. 



PHOSPHORESCEXCE OF THE SEA. 337 

b C v at th r e ed wX a nf le th ^ t G SP ? y ° f u the S6a ' and ln the foam c ^ed 
tL f a Y he Shl ^ When the water is sl % h % a ?itated bv 
J^ lnds , ° r ? urre f s ' ?* s ^ond is a flash of pile light of mi 

ZT J J m ?T bUt w en intenSe eno "S h t0 ^minate the water 
necuLrtn If S r eral f6 f V ^ third ' 0f rare occurrence, and 
peculiar to gulfs bays, and shallows, in warm climates, is a dif- 
fused pale phosphorescence, resembling sometimes a sea of milk, 

rrlnt^T?\l n ' Stat t°5 lgne ° lTs ^^ion; the fourth 
presents itself to the astonished voyao-r under the aDuernon of 
thick bars of metal of about half a foot in le^h%^Tto2hL 
ness, scattered over the surface of the ocean,'some%isin, up an 1 

decnne U1 anVdT m0US M ^ ' ? ^ Ye ™ {n in view ' whTle ^hers 
th Zrf^ r PPea l :> and the fifth variet y is in distinct spots on 
the surface, of great beauty and brilliancy. The lio-ht of the first 
vanety is more brilliant and ccndensecUhan tha of any of the 
rat of ft T J r, Ch reSe ^ leS eVer ^ wa ? the ™d gold and silver 
produced bvTS m t ™ S ^^ with *e third kind axe 
smalls wl, F d i °^T an0US minUte cr ^taceous animals, the 
ITnlf . and Mol J usca > and Perhaps some Annelid* the 

second appears to proceed from the gelatinous Medusa, of a larger 
b P n'frp. P.y rosom f are the cause of the fourth kind, which mav 
the°Cane ofr SS !f ^ VeMel8 h °^ t0 Ma ' or *e eastward of 
the line PG ' occumn 2 in the calm latitudes near 

in ^Z^JT^Z Indlc ^™ insect somewhat resembling 
nch P 1 ^ 00 S^se ft^), and about one-third of an 

o be Wtef to Z ltS the - laSt T iety «™ m erated, which appears 
' Jr l1 ? 1 lted t0 £ e se as situated to the north and west of a line 

tZ^^A G °° d H ° pe t0 the — extremity ^f 

4m£ S ° m? fl ° Wer 1 S haVe been ^marked to emit flashes of li ff ht 
while growing on the plants to which they belong These mink- 

Z2t»r gS S r etlmeS are P erceived ° f a ^™me eveni" in 
warm close weather issuing from the petals of the African "and 
the common marygold, the nasturtium, and the tuberose. 

stances f^SifS ^^^ ^u ° Ut H 2 ht Under P articular ^^- 
S crVstTl wn i t CaSe W ! th S ° me diam01lds > »d varieties of 
rock crystal, which become luminous on being removed into a 

fh Bo W ter f P T re t0 . the ra ^ S ° f the sun - W ^t s called 
he Bolognian phosphorus, is artificially prepared by mixing into 
a paste, with gum tragacanth, powdered sulphate of bSyfes, or 

ma^auLs'ttt 3 ? 81 ' 1 - tieS ,° f ,umi,10 ^ness are exhibited at sea I 
*v nac causes the first variety ? 

How is the fourth kind to he explained ? 

tfr of i he ocea " " the pyrosoma found ? 
Where the sapph.rina indicator ? 

UnKr, 8 8 - re kn ° Wn t0 emit l^nous flashes ? 

What ar^ciTST^ ? a P ertain mine, '* ls »™^' * emit light > 

al umtat.ons of these substances have been prepared 



Thompson's Zoological Researches and Illustrations. 1832 T^ 
2 F 



338 optics. 

ponderous spar, and dividing the mass into thin cakes, which are 
to be carefully calcined in an open fire and suffered to cool slowly; 
they then shine in the dark after being exposed to the sun. 

18. Canton's phosphorus, which consists of sulphuret of lime ; 
and Baldwin's phosphorus, which is nitrate of lime, have analo- 
gous properties ; and oyster-shells, calcined by putting them into 
a coal or charcoal fire, for about an hour, and when cold taking off 
a thin scale from the inside, will be found to be become phospho- 
rescent. There are minerals which are rendered luminous in the 
dark by exposure to a temperature of red heat, as phosphate of 
lime, from Estramadure, and some kinds of flour or Derbyshire 
spar, fetid carbonate of lime or swinestone, quartz, and ponderous 
spar. 

19. Light may be elicited from violent friction or collision of 
incombustible bodies, just as fire is from flint and steel. Thus 
bright sparks may be produced by striking one piece of common 
flint or rock crystal against another ; rubbing together two pieces 
of bonnet-cane will cause the emission of light, in consequence 
of the epidermis or scaly coating of the cane being composed of 
siliceous earth ; and loaf sugar yields a pale light, from the col- 
lision of two lumps in the dark, the effect being merely the exhi- 
bition of phosphorescence, for though sugar is an inflammable sub- 
stance, the luminous appearance is unaccompanied by combustion. 

20. Light, considered as the cause of vision, or the medium by 
which objects become perceptible to sight, exhibiting a variety 
of tints to the eye, has generally, since the publication of Sir 
Isaac Newton's theory of light and colours, been ascribed to the 
emission of a peculiar ethereal fluid from the sun and all other 
luminous bodies. This subtile fluid or ether was supposed to be 
perpetually streaming in all directions from the sun and fixed stars, 
travelling with a velocity 900,000 times that of sound through 
the air, and yet consisting of particles so extremely minute as to 
pass through the densest substances without at all altering their 
structure, or interfering during their progress in the slightest de- 
gree with each other. Descartes, who died in 1650, had advanced 
a different hypothesis to account for the action of light, founded 
on the admission of the existence of an ethereal fluid, not subject to 
amotion of translation, or passage from one part of space to another, 
but capable of being thrown into the state of undulation by the 
impulse of luminous bodies, and the undulating motion being in- 
definitely extended, would obviously propagate the influence of 
light through any given space. 

21. The theory of undulation, as it is termed, was adopted and 
improved by Huygens, the contemporary of Newton, whose sys- 

By what mechanical means may combustible bodies be made to emi 
light ? 

Is any real combustion produced in these cases ? 

What theories did Newton advance to account for the phenomena ot 
Ught and vision ? 

At what rate did he find it necessary to suppose light to travel 1 



CAUSE AND MODE OF PROPAGATION OF LIGHT. 339 

tern of emanation or emission of light, proposed by the latter, prin- 
cipally through the authority of his great name, prevailed almost 
universally till about the middle of the last century, when it was 
attacked by Leonard Euler, who, in his " Letters on different sub- 
jects of Natural Philosophy, addressed to a German Princess," 
has pointed out the difficulties which occur in attempting to ex- 
plain the phenomena of light according to Newton's doctrine or 
theory of emanation, and has advanced many striking arguments 
in favour of the theory of undulation, showing the analogies be- 
tween the modes of propagation of light and sound, and demon- 
strating the general agreement of the hypothesis with those facts 
which constitute the basis of optical science. Euler, however, 
gained but few converts among his scientific contemporaries, and 
the opposite theory was generally admitted as correct till about 
the beginning of the present century, when Dr. Thomas Young, 
in the Bakerian Lecture, read before the Royal Society, in 1801, 
entered into an elaborate disquisition concerning the theory of light 
and colours ; and deduced from the principles laid down by New- 
ton himself, the three following hypotheses : 

22. 1. That a luminiferous ether, rare and elastic in a high de- 
gree, pervades the whole universe. 2. That undulations are ex- 
cited in this ether whenever a body becomes luminous. 3. That 
the sensation of different colours depends on the frequency of 
vibrations excited by light in the retina. To these he added a 
fourth hypothesis, assuming that all material bodies have an at- 
traction for the ethereal medium, by means of which it is accumu- 
lated within their substance, and for a small distance around them, 
in a state of greater density but not of greater elasticity.* 

23. Subsequent discoveries have tended to confirm the theory 
of undulation, which affords a more unobjectionable mode of ex- 
plaining the phenomena of polarized light, and other appearances, 
than is furnished by the theory of emanation ; and the former has 
been embraced by the most distinguished philosophers now living 
or recently deceased; as Fresnel, Arago, Sir John Herschel, Sir 
D. Brewster, and others, who by their own discoveries have con- 
tributed to extend the boundaries of science. 

24. The propagation of light always takes place in right lines, 
projecting on every side from luminous bodies. Such radiating 
lines or rays, diverge from each other in their passage, forming 
what is called a pencil of light, as exhibited in the marginal figure. 

What substitute tor the theory of emission was adopted by Descartes, 
Huygens, and Euler ? 

"W hat three positions were established by Dr. Young on this subject ? 

What relation did he assume to subsist between the luminiferous ether 
and common matter i 1 

Which of the two theories appears at present to possess the greater 
number of advocates among the cultivators of this science ? 

In what lines does the propagation of light take place ? 

* See Philos. Transact, for 1802 ; and Abstract of Papers in the Phil. 
Trans., vol. i. pp. 64, 65. 



340 

A similar effect 



OPTICS. 

may be- produced by admitting into a darkened 
room, through a minute aperture in a win- 
_ dow-shutter, the light of the sun which would 
be perceived proceeding- in a diverging 1 bun- 
dle or pencil of rays ; and on presenting to 
it a flat board, a luminous image would be 
formed, increasing in diameter with the in- 
crease of distance from the aperture at which 
the plane was held, and which, by variously 
inclining the plane, might be made to assume elliptical or other 
curved figures. 

25. Images of variously-shaped bodies seen by light thus ad- 
mitted through a small opening are always in a reversed position, 
in consequence of the obliquity or divergence of the rays of light. 





That this effect must take place will be readily perceived from 
the preceding figure, which shows that the rays in passing through 
the opening must cross each other, and thus rays coming from the 
superior parts of objects, impinge on the relatively inferior portion 
of the plane, and those from the higher parts strike on that portion 
of the plane below the other rays : the spectra or images produced 
must consequently be inverted. 

26. It is stated above that the dimensions of the images thus 
formed decrease in proportion to the distance from the opening at 
which they are situated. Thus if the plane on which the image 
of an object is received, be placed at exactly the same distance 
before the aperture, as the object stands behind it, the size of the 
image will coincide with that of the object, for the pencils of rays 
on either side would be alike. If, however, the plane be removed 
nearer the aperture than before b} r one-half, the image will be but 
one-fourth of the size of the former ; at one-third the distance, its 
size would be one-ninth ; at one-fourth the distance, one-sixteenth ; 
the diminution taking place in the ratio of the squares of the dis- 
tances of the plane from the aperture. The intensity of light di- 
minishes in the same proportion : thus suppose a candle to be 



By what experiments can this he proved ? 

How is the rectilinear course of rays proved by the images formed in 
a dark room by light admitted through a simple aperture ? 

What ratio will the size of such an image have to the distance of the 
screen from the aperture ? 

How does the intensity of light vary with the distance of the radiant 
or source of light ? 



RELATIVE INTENSITY OF LIGHT. 341 

placed at the distance of one yard from the face of a dial or time- 
piece, the light thrown on it may be represented by the number 
1 ; if then it be removed back to two yards, the light will be but 
£ as much as before; at 3 yards 1-9, at 4 yards 1-16, at 5 yards 
1-25, at 25 yards 1-625. 

27. This reduction of light, in proportion to the distance of the 
luminous body, is the necessary effect of the divergence and con- 
sequent dispersion of the radiant pencil ; and hence it may readily 
be conceived, that an inconsiderable light can only be visible at a 
comparatively trifling distance, and that its influence in rendering 
non-luminous objects visible, must be limited to a much shorter 
distance than the extreme point at, which its light will be per- 
ceptible. 

28. The apparent size of all visible objects is to be explained 
on the same principles with those that govern the formation of 
images by light transmitted through an aperture, as just described. 
When we take a view of an illuminated body, its image becomes 
traced in shadow, exhibiting, however, its proper colours on the 
retina, a nervous membrane that lines the interior surface of the 
eye. A more particular description of the structure and apparent 
uses of the different parts of the organ of vision will be introduced 
after the nature and causes of the refraction of light have been ex- 
plained ; but the relation between visible images of objects and 
the angular distances of the objects themselves may here be con- 
cisely pointed out. 

29. From what has been previously stated concerning the dimi- 
nution of the light of a pencil of rays in proportion to the distances 
of the point whence they diverge, it must be evident that the 
nearer to the eye any object may be placed, so much more nume- 
rous will be the rays of light passing from it which can act upon 
the eye so as to form the image on the retina. The number of the 
rays indeed will increase or decrease as the squares of the dis- 
tances of objects, after the manner already described. This, how- 
ever, is to be understood as the law that regulates the propagation 
of light simply and independently of the medium it traverses ; for 
air, the most transparent of bodies, interrupts in some degree the 
passage of light through it, as elsewhere observed ; and therefore 
the apparent dimensions of objects must be considerably influ- 
enced by the nature of the medium through which they are be- 
held.* 

30. The angle formed by the crossing of the rays of light pass- 
ing from the opposite extremities of a visible object is called the 

What causes this variation ? 

How is the apparent size of objects dependent on their distance ? 
How must the apparent brightness of an object be affected by its near- 
ness to the eye ? 

What is meant by the angle of vision? 

* See the subsequent part of this treatise, relating to the Refraction of 
Light. 

2 f2 



342 optics. 

angle of vision. Now that angle will be relatively very contract- 
ed when the radiating lines are emitted from an object extremely 
minute, or from one placed at a great distance. Thus there are 
insects too small to be visible to the naked eye even when brought 
as near to it as possible ; and some objects of immense size, as 
the fixed stars, each of which probably is many thousand times 
larger than the earth, appear as mere points from the remote situ- 
ations they occupy; while there are doubtless multitudes of other 
stars yet more remote, and therefore quite invisible, even when 
the heavens are surveyed through the best telescopes. Unless 
the angle of vision be more than one second of a degree, the object 
whence the rays proceed will not be visible, without it be very 
strongly illuminated. 

31. The velocity of light is so great that it was long supposed 
*,o pass instantaneously through any given space; and though it 
nas been ascertained that it occupies a certain time in its passage 
proportioned to the distances traversed, yet so rapid is its appa- 
rent motion, that in observing the effect of light at places a few 
miles distant from each other the time need not be taken into the 
account. The rate at which light is propagated was discovered 
by Olaus Roemer, in making observations on the eclipses of the 
satellites of Jupiter I 

32. If the transmission of light were instantaneous, it must be 
obvious that the reflected light of the sun would take up no more 
time in passing from any one of the planetary bodies to the earth, 
when they are farthest from us, than it does when they are near- 
est; and as the situation of the earth with respect to the other pla- 
nets is different in different parts of her orbit, the satellites of Ju- 
piter, on emerging from the shadow of that planet, would be seen 
as quickly when the earth was in one part of her orbit as in ano- 
ther. But this is by no means the case ; and the effect of the 
transmission of light is such, that when the earth is between Ju- 
piter and the sun, the satellites, after being eclipsed, are perceived 
rather more than eight minutes sooner than they ought to appear 
according to the time as calculated by the most accurate tables ; 
and when the earth is in the opposite part of her orbit, so that the 
sun is between this planet and Jupiter, the satellites emerge about 
eight minutes later than the calculated or mean time. 

By what two circumstances may that angle be diminished till the ob- 
ject becomes imperceptible ? 

Give some illustrations of both cases. 

What is generally the least angle under which an object can be seen ? 

What was formerly thought of the motion of light ? 

Why do we make no account of the time occupied by light in travers- 
ing distances on the earth's surface ? 

How would the instantaneous transmission of light through space ena- 
ble us to see the heavenly bodies in different parts of the earth's orbit ? 

What is found to be the fact in regard to Jupiter's satellites ? 



VELOCITY OF LIGHT. 



343 




33. In the annexed diagram, let S re- 
present the sun, A and B the earth in dif- 
ferent parts of her orbit, J, Jupiter, D, his 
nearest satellite entering- the shadow of 
that planet, and C, the same satellite, 
emerging from the shadow. Now the time 
of the commencement or termination of an 
eclipse of the satellite, as stated from cal- 
culation in tables, is the instant at which 
the satellite would appear to enter or^ 
emerge from the shadow, if it could be 
seen by an observer from the sun : and it 
is found from repeated observation, that 
the eclipse takes place about 8 minutes 
earlier than the calculated period, when 
the earth is in the nearest part of her orbit, 
as at A, and 8 minutes later when she is 
in the opposite part of her orbit, as at B. 
Hence it will be apparent that light takes 
up 8 minutes in passing through a space 
equal to half the diameter of the earth's orbit, or the distance be- 
tween the earth and the sun, which is ninety-five millions of 
miles ; so that it moves at the rate of 95,000,000 -f- 8 X 60= 
197,916, nearly 200,000 miles in one second. 

34. The aberration of the fixed stars also shows with what 
speed light is propagated ; Dr. Bradley having ascertained that 
this phenomenon depends on the motion of the earth in her orbit, 
in connexion with the velocity of light. The effect thus produced 
on the apparent places of the fixed stars at different times, termed 
aberration, is familiarly explained by Professor Robison. He ob- 
serves, that if hailstones were falling perpendicularly, they would 
pass freely through a tube held steadily in a vertical position; but 
if the tube were moved round in a circle while the hailstones were 
falling they would impinge against its side, unless the tube were 
inclined forward, at an angle of 45 deg., supposing the velocity 
with which the tube was moved was equal to that of the falling 
hail. "In the very same manner, if the earth be at rest, and we 
would view a star near the pole of the ecliptic, the telescope must 
be pointed directly at the star. But if the earth be in motion 
round the sun, the telescope must be pointed a little forward, that 
the light may come along the axis of the tube. 



What is the true time of commencement or termination of the eclipse 
of one of those satellites ? 

Construct and explain the diagram, showing the velocity of light. 

How long does it require to traverse a semi-diameter of the earth's orbit? 

How far will it travel in a second ? 

On what does the aberration of the fixed stars depend ? 

By what supposed arrangement of apparatus may the aberration of 
light be illustrated ? 

What must the absolute direction of a telescope be in regard to the 
position of the body viewed ? 



344 optics. 

35. "The proportion of the velocity of light to the supposed ve- 
locity of the earth in her orbit is nearly that of 10,000 to 1 : there- 
fore the telescope must lean about 20 sec. forward. Half a year 
after this, let the same star be viewed again. The telescope must 
again be pointed 20 sec. ahead of the true position of the star : 
but this is in the opposite direction to the former deviation of the 
telescope; because the earth, being now in the opposite part of 
her orbit, is moving the other way. Therefore the position of the 
star must appear to have changed 40 sec. in the six months. It 
is easy to show that the consequence of this is, that every star 
must appear to have 40 sec. more longitude when it is on our me- 
ridian at midnight than when it is on the meridian at mid -day. 
The effect of this composition of motions, which is most suscepti- 
ble of accurate examination, is the following. Let the declination 
of some star near the pole of the ecliptic be observed at the time 
of the equinoxes. It will be found to have 40 sec. more declina- 
tion in the autumnal than in the vernal equinox, if the observer 
be in the latitude of 66 deg. 30 min. ; and not much less if he be 
in the latitude of London. Also every star in the heavens should 
appear to describe a little ellipse, whose longer axis is 40 sec."* 

36. As the total absence or privation of light produces darkness, 
so the partial defect of light occasions shade; and when any 
opaque body interrupts the passage of the ra)^s of light, the figure 
of that body or its outline surrounding a dark area will be formed 
on any plane surface beyond the opaque body, constituting its 
shadow. The depth or darkness of the shadow is always in di- 
rect proportion to the intensity of the light ; and if an opaque body 
be illuminated by several lights at once, differently situated, as 
many shadows will be formed as there are lights present; as 
may be observed with respect to any object in a room where two 
or more candles are burning. If the luminous body be larger 
than the opaque body that intercepts its rays, the shadow will be 
in the figure of a pyramid the base of which will be equal to the 
surface of the opaque body, and its extent will depend on the dis- 
tance at which the luminous body is situated from that which in- 
tercepts its light. 




What is the proportion between the velocity of light and that of the 
earth's progressive motion ? 

How much must a telescope be inclined forward of its real object in 
order to see a remote luminary ? 

Why will it appear to be again in advance of its true position at the 
end of half a year ? 

On what is the intensity of shadows dependent ? 

What will be the form of shadows when the radiant is larger than the 
intercepting surface ? 

* Elements of Mechanical Philosophy, 1804, vol. i. pp. 264, 265. 



CAUSE OF SHADOWS. 



345 



37. Thus, in the preceding diagram, suppose S to represent the 
sun, V the planet Venus, and E the earth; then if the two planets 
were of equal size, Venus being nearer than the earth to the sun 
would cast a shorter conical shadow than our planet. 

38. If a shadow be formed by an opaque body of exactly the 
same dimensions with the luminous body whose rays it interrupts, 
the shadow will be a cylinder of an area equal to that of the two 
bodies, and extending infinitely in length. But if the luminous 
body be smaller than the opaque body the shadow will be a trun- 
cated pyramid, the larger base of which must be at an infinite 
distance. In the former case the rays of light will proceed in pa- 
rallel lines till they are intercepted, and the consequent shadow 
will preserve the same dimensions throughout its indefinite extent; 
and in the latter case the rays will be divergent, and the shadow 
formed will increase in dimensions in proportion to the distance 
between the two bodies. 




39. This will further appear from considering the relative di- 
mensions of the bame figure when the shadow is thrown on a 
plane surface at different distances from the source of light. Thus 
let A be an object illuminated by the light of a candle, and B, C, 
D, E, be a succession of screens, B being the nearest, and E the 
most distant; the former, therefor, will have the smallest shadow, 
and the latter the largest. 

40. The proper shadow or dark outline of an opaque body, 
formed when it intercepts the rays of light from a luminous body, 
is always encompassed or bordered by a kind of demi-shadow, or 

01//^ as it is termed, penumbra.* Thus, 

in the annexed diagram, let S re- 
present the sun, or any other source 
of light, and A B any opaque body, 
the true or proper shadow of which, 
on the plane M N, will be termi- 
nated by the tangential line C A F, 
and the space B A F will be entirely 
shaded; but the penumbra will ex- 
tend from F to I, including the space 

How is this illustrated in the solar system ? 
Exhibit and explain the diagram on this subject. 

What form will the darkened space possess when the opaque body and 
the radiant are of the same size ? 




* From the Latin pe7ie, almost, and umbra, a shadow 



346 



OPTICS. 



F A I, which will be partially enlightened, the shade gradually di- 
minishing as it recedes from F towards I, where it will be terminat- 
ed by the second tangent E A I. 

41. An eclipse of the sun being occasioned by the interposition 
of the opaque body of the moon between the earth and the sun, 
the proper shadow will be a frustum of a cone converging from 
the moon towards the earth, and there will be a fainter shadow or 
penumbra surrounding the former. This is shown in the annexed 
figure, where S represents the sun, M, the moon, and L, the earth ; 




the dark space is denoted by the inner conical shadow, beyond 
which, on either side, extends the penumbra. 

42. Shadows are in general regarded as being perfectly black, 
as they certainly must be where the light of a luminous body is 
completely excluded by an opaque body placed before it. But 
shadows, as they commonly appear, are found to vary in colour as 
well as intensity, according to circumstances. Thus, the shadows 
produced by the sun at different hours of the day, and those caused 
by different sorts of lights, if attentively examined, will be per- 
ceived to consist of green, blue, violet, or red tints more or less 
sullied by black. 

43. The figure of the enlightened part of an opaque body, seen 
by means of a fixed light, depends on the relative position of the 
light and of that of the observer. 

C/^ss Let L, in the marginal 

figure, be the place of the 
luminous point, O the sit- 
uation of the observer : 
then, an opaque sphere 
placed at A would not ap- 
pear at all enlightened; 
at B, the enlightened por- 
tion of the sphere would 
assume the form of a cres- 
cent; at C it would be a 
eemi-circle ; at D it would approach to a circle ; and at E the circle 
would be complete. The phenomena would be repeated, but in 

What will be its form, 
one ? 

What is meant by a penumbra ? 

Explain it by diagram. 

What is the form of the umbra, or proper shadow in eclipses of the 
moon ? 

What is that of the penumbra ? 

What variety appears in the colours of shadows? 

How are the successive appearances of the moon to be explained ? 

Draw and describe the diagram for its phases. 




if the opaque body be larger than the luminous 



REFLECTION OF LIGHT. 34? 

inverse order, in proceeding- through the opposite positions, from 
E to A. The extent of the enlightened part visible from the point 
O, is determined by the tangents drawn from the small sphere to 
the points L and : thus a b marks the enlightened part which is 
visible of the sphere D. 

44. This diagram and description will serve to explain the 
phases of the moon, or her various appearances, as enlightened 
by the sun, and viewed from the earth in different parts of her or- 
bit. That satellite being- invisible at the chang-e, or new moon, as 
at A, and afterwards exhibiting more and more of her surface till it 
becomes a complete circular disk, or full moon, as at E ; after 
which the waning moon travels on to A, whence a fresh succession 
of changes takes place. 



CATOPTRICS. 



45. Besides the general effect of light in rendering visible all 
objects within the influence of the rays extending from luminous 
bodies to those around them, there are peculiar phenomena which 
take place when the rays are thrown on substances presenting very 
bright or smoothly polished surfaces. For in such cases, if the 
surfaces are very highly polished, they are no longer visible when 
thus illuminated, but exhibit perfect pictures of any objects placed 
in front of them, that is between the light and the polished surface. 
The effect just described is one with which all adult persons in 
civilized countries are so familiarly acquainted, in consequence of 
the general use of mirrors or looking-glasses, that they cease to 
excite wonder or observation; but brute animals, ignorant savages, 
and doubtless very young children, when they behold for the first 
time an image in a mirror, must suppose it to be a real object. 

46. The effect of such an exhibition on a game-cock has been 
often noticed, and that brutes and children may be thus deceived 
may easily be admitted ; but it might be apprehended that a savage 
coul'd hardly be ignorant of the effect of light on the smooth sur- 
face of clear water, and that he would therefore view without sur- 
prise his own image in a looking-glass. This, however, is not 
always the case ; and a modern traveller relates an amusing story 
of a savage, who, on being shown his face in a pocket glass, be- 
came excessively alarmed, and could by no means be induced to 

At what point does the moon become invisible from immersion in the 
sun's rays ? 

How may an opaque surface be rendered invisible ? 

What familiar illustration of the case is afforded by the use of mirrors ? 

What evidence have we that only the image formed by the mirror is 
really visible ? 

What confirmation do travellers afford of the correctness of this suppo- 
sition in regard to mirrors ? 



348 



OPTICS. 



approach again either the glass or its owner, conceiving that the 
individual who could take his likeness, by means of his mysterious 
machine, might perhaps appropriate his proper person, and keep 
him and sell him for a slave. 

47. The common term reflection has been adopted to denote the 
direct effect of light in producing images of bodies in their proper 
places, and also the indirect effect of light in forming, by means 
of polished surfaces, images of bodies in some place or places 
different from that where they appear by direct light. The latter 
kind of reflection alone, or that caused by variously-formed mirrors, 
or more or less perfectly polished surfaces, constitutes the subject 
of that branch of science called Catoptrics.* Reflecting surfaces 
may form images, the apparent situation of which will be more 
distant from the observer than the surface or mirror itself, as hap- 
pens in the case of common looking-glasses, or convex mirrors; 
or the images may be formed between the eye of the observer and 
the reflecting surface, and may therefore appear in the air, as 
will be perceived in, some cases where concave mirrors are used. 
Other singular effects may be exhibited by means of- cylindrical 
or conical mirrors, or by various arrangements of mirrors, and by 
combinations of them with other optical glasses. 

Reflection from Plane Surfaces. 

48. Rays of light are reflected according to the same laws that 
regulate the motions of perfectly elastic solids ; for a ray imping- 
ing on a reflecting surface will be returned or reflected in such a 
manner that the angle of incidence shall be exactly equal to the 
angle of reflection. f Hence if a ray of light falls horizontally on 
a plane mirror held vertically, it will be reflected in the same right 
line; but if it falls obliquely, it will be reflected with the same 
that is, the returning line and the line of 
similar angles with a perpendicular drawn 



degree of obliquity ; 
incidence will form 
between them. 

E P 



> 




49. This may be shown by admitting 
through a small aperture, into a dark cham- 
ber, a ray of light, and receiving it on a me- 
tallic mirror A B ; if it fall obliquely in the 
direction C D, it will be reflected in the line 
D E, and will form a lucid spot at E on a 
plane properly placed to meet it. Since all 
rays falling on a reflecting surface relatively 
preserve, after reflection, directions corre- 

To what two sets of phenomena is the term reflection applied ? 
What is meant by catoptrics ? 

In how many positions, with reference to their distance from the eye, 
may images be formed by reflecting surfaces? 

According to what laws are rays of light reflected? 
How may this be experimentally demonstrated ? 

* From the Greek k*tostt^ou, a mirror. 
t See Treatise on JfcchzrJcs, Xo. 31. 



EFFECT OF PLANE MIRRORS. 



349 




sponding with those they had previously, therefore a ray falling on 
a mirror perpendicularly would be reflected on itself, and conse- 
quently could produce no lucid image. 

50. The relative position of the image of 
an object as seen in a reflecting plane will be 
such that every part of the image will appear 
as far behind the plane as the object itself is 
before it. Let A B represent a plane mirror, 
and E F any object, as an arrow ; then draw, 
from the points E and F, the perpendiculars 
E G and F H to the surface of the mirror, 
and produce those lines to e and /, so that 

ff EG shall be equal to e G, and FHto/H, 
and ef will be the position of the image 
which will be exactly equal to the object, as 
the quadrilatera. figure G ef H will be equal to the quadrangle 
G E F H. From inspection of this figure it will be perceived, 
that the rays of light proceeding from that part of the object nearest 
to the surface of the mirror will be reflected so as to form the part 
of the image nearest to the plane of the mirror in the opposite di- 
rection. Hence when trees or buildings, or any other objects, are 
reflected from an horizontal plane, as the surface of a pond or a 
smooth stream of water, they will appear inverted ; for their lower 
parts being nearest to the reflecting surface are seen immediately 
within it, while their tops seem to hang downwards, or to extend 
deeper beyond the surface. 

51. When a mirror, C, in the annexed 
-.^>,. figure, is inclined forward at an angle of 45 

b deg. an object A B, if placed in a vertical 
position, will form an horizontal image a b; 
and if the position of the object be horizon- 
tal, that of the image will be vertical. 

52. A person standing before a plane mir- 
ror placed vertically opposite to him, will not 
perceive the image of his whole person, if 
the length of the mirror be less than half his 

height. But if the upper part of the mirror be inclined forward, 
more of the image will become visible, in proportion to the dimen- 
sions of the mirror, than when it is placed vertically; and hence 
a person may view himself from head to foot in a looking-glass 

Explain the diagram relating to the incident and reflected rays. 

Into what line will a ray falling perpendicular to a reflecting surface be 
reflected ? 

Explain the relative position of parts of an image formed by a reflect- 
ing plane. 

Why do trees, buildings, or other objects seen by reflection from a sur- 
face of water, appear inverted ? 

How may a vertical object be made to produce a horizontal image ? 

How long must a vertical plane minor be, in order that the whole 
person may be seen by an eye immediately in front of it ? 

What expedient enables us to see the whole person in a small mirror } 
2G 




350 optics. 

of a moderate size, by giving it a due degree of inclination, but 
then the image as well as the mirror will appear in an oblique 
position. 

53. Any one looking into a fixed mirror, and at the same time 
stepping backwards or advancing forwards, would perceive his 
image also to recede or approach, but with double the velocity of 
the actual motion. This will be understood by recurring to what 
has been stated relative to the angle under which the image is 
perceived. 

54. A number of images may be formed and peculiar effects 
produced by means of two mirrors, either inclined or parallel, and 
opposite to each other, for the image of an object which is delinea- 
ted behind one mirror may thus serve as an object to be reflected 
from the surface of another mirror. 

55. If any object, as M, N, be 

^v- "^>f placed between two plane mirrors in- 

/m^t /\ clined towards each other at an an- 

' T\Nsa?/ \ gle A C B, several images will be 

/ \ /iik \ P erc eived, all situated in the circum- 

/ m \o/ ^>vvJ ference of a circle. This may be de- 

b\ -rat* /r ••%""U monstrated by drawing- the image in 

l » m / \ ^>^ m \ its place behind each mirror, and con- 

\ I * $i0jir I sidering each image as forming an 

\ \J sS^^'"\ / object in its turn, the image of which 

^^pm// •>/ * s a ^ so to De drawn. Thus it will be 

&^-^ <^o>' perceived that the image of M N in 

the mirror A C is m n, while its 
image in B C is M 7 N 7 ; and in the same manner the image formed 
by the reflection of the first image m n in b C will be M" N", while 
the image of M' N 7 in a C will be m'n'. It will further appear 
that m" n" is the image of both M" N" in the mirror b' C, and of 
ml n' in the mirror a' C, one of the images covering the other, if 
the angle A C B be 60 degrees, or the sixth part of a circle, as 
in the diagram ; but, if the angle be any greater or less, the image 
m" n" will be two-fold; that is, the two images will not ex- 
actly coincide. On this principle is formed the Kaleidoscope,* 
invented by Sir D. Brewster, and by means of which the reflected 
images, viewed from a particular point, exhibit symmetrical figures 
under an infinite variety of arrangements of beautiful forms and 
colours. 

5G. If the two mirrors are placed opposite and parallel to each 
other, an indefinite multitude of images will be perceived, becoming 
more and more indistinct by repeated reflection, till at last they 

How may the image be made to advance or retire ? 

How may the image of one reflection be made the object of another ? 

Explain this by the diagram. 

What optical toy is constructed on the principle of multiplied reflection; 

What appearance results from reflections between parallel mirrors ? 

* From the Greek k^-. ; , beautiful, e«Soj, a form, and i>.s»s:,., to view. 



ATMOSPHERIC REFLECTION. 351 

vanish in obscurity. This effect may be advantageously observed 
m an apartment where two mirrors are fixed on opposite sides of 
it, w^ith a lustre, or some such object between them. One of the 
rooms at Fonthill Abbey, built by the eccentric Alderman Beckford, 
was wainscoted, as it were, with mirrors of plate-glass ; and 
thus it presented to the spectator an interminable vista on ever}'' 
side, filled with a seemingly infinite multiplicity of objects. 

57. Common mirrors are formed of glass, to the back of which 
is attached an amalgam or mixture of tin and quicksilver, which 
adhering to the surface of the glass forms a smooth polished plane, 
capable of reflecting the rays of light which impinge on it more 
abundantly than almost any other kind of mirror. The principal 
reflecting surface in this case is that where the metallic covering 
joins the back part of the glass ; and the image there formed under 
ordinary circumstances is so bright and distinct as to prevent any 
other from being perceived. If however, a lighted candle be held 
before a glass mirror, so that its rays may fall on the glass obliquely, 
several images may be perceived ; as a faint one at the outer sur- 
face, another much more intense just behind the former, and seve- 
ral others gradually receding, and becoming fainter and fainter, till 
they vanish in the distance. The first faint image is formed by 
reflection from the outer surface of the glass, the second, or prin- 
cipal image, at the surface of the amalgam, and the others by 
reflection within the glass. These interfering secondary images, 
though of no importance in a common mirror, would produce con- 
fusion in more delicate optical instruments, such as the reflecting 
telescope, the mirrors of which therefore are constructed entirely 
of polished metal, which, presenting only one reflecting surface, 
affords a single image. 

58. Among the natural phenomena produced by the reflection 
of light, by far the most important is that of atmospheric reflec- 
tion, for without it few objects would be visible excepting those 
on which the rays of the sun might fall in a direct line between 
that luminary and the eye. But the rays of light falling on the 
particles which compose the atmosphere are thence reflected in 
every direction, and thus daylight is produced even when the 
whole visible hemisphere is covered with clouds, and the face of 
the sun is hidden from our view. But for reflection, all opaque 
bodies would cast perfectly dark shadows ; and on turning our 
backs to the sun the objects before us would be involved in the 
deepest obscurity. 

59. Some of the less usual phenomena depending on atmos- 
pheric reflection are extremely curious, as that called the Mirage, 

Where has this experiment been exhibited on a grand scale ? 

How are common mirrors constructed ? 

What part does the glass act in the formation of images ? 

How are the numerous images, visible in an oblique direction to the sur- 
face of the mirror, produced ? 

Why are not glass mirrors employed for reflecting telescopes ? 

What would be the effect of opaque bodies, if the atmosphere were des- 
titute of reflecting power t 



352 optics. 

and a variety of aerial spectra of an analogous kind. The mirage is 
generally perceived on sandy plains in hot climates, as in E gypt and 
in South America ; and it has been often described by travellers. 

60. In the middle of the day, when the sun shines on the level 
surface of the sand, the appearance of a sheet of water is obser- 
ved at the seeming distance of about a quarter of a mile; the de- 
ception being so complete, that any person unacquainted with 
its cause would inevitably suppose he was approaching a lake or 
river. Like real water, the spectral lake reflects objects around, so 
that houses, trees, and animals, are perceived with the utmost dis- 
tinctness in this singular mirror. As the observer advances, the 
visionary stream recedes, still keeping at the same apparent dis- 
tance, but with changes of scene, by the disappearance of images 
first beheld, and the formation of new ones from other objects, 
as they successively become liable to reflection. 

61. The French philosopher Monge, who witnessed this phe- 
nomenon in Egypt, published a satisfactory explanation of it in 
the first volume of the Decade Egyptienne ,- and about the same 
time a similar exposition of the cause of it was given by Dr. 
Wollaston, in the London Philosophical Transactions. The latter 
also produced an artificial mirage in the heated air over a mass of 
red-hot iron ; and he observed the same appearance in bodies seen 
across the surfaces of two differently refracting fluids placed one 
above the other in a transparent vessel. 

62. He thus accounts for the phenomenon : in the middle of 
the day, the sandy soil becoming very hot, the stratum of the 
air in contact with it acquires a very elevated temperature, and 
hence, being dilated, its density is found inferior to that of the 
strata immediately above it, and the luminous rays which fall 
on this dilated stratum, at an angle comprised within a cer- 
tain limit of 90 degrees, are reflected at its surface as from a mir- 
ror ; and they convey to the eye of the observer the reversed 
image of the lower parts of the sky, which are then seen on the 
prolongation of the rays received, and consequently appear below 
the real horizon. In this case, if nothing corrects the error, 
the limits of the horizon will appear lower and nearer than they 
really are. 

63. If any objects, as villages, trees, or the like, render it evident 
to the observer that the limits of the horizon are more remote, and 
that the sky is not so low as it seems, the reflected image of the sky 
will appear to form a reflecting plane of water. The villages and 
the trees will emit rays which will be reflected just as rays 

How is the mirage formed ? 

Give some account of that appearance. 

How may the effect be imitated ? 

What explanation did Wollaston give of that phenomenon t 

How is the imagination led to the supposition that the reversed image 
of the lower part of the sky is nearer and lower thau the true visible ho- 
rizon ? 

How does it appear that trees, buildings, &c, ought to appear reversed 
in the inverted image of the sky ? 



AERIAL SPECTRA. 353 

would have been if coming- from the part of the sky intercepted by 
them. And these rays will produce a reversed image below the 
objects seen by direct rays. The limit at which the luminous 
rays beg-in to be reflected being constant, and the rays that form 
the largest angle with the horizon appearing to come from the 
point nearest to the spot where the phenomenon commences, this 
point must be at a constant distance from the observer : hence if 
he advances, the border of the lake will seem to recede, as actually 
happens. 

64. MM. Jurine and Soret, in September, 1818, observed, on 
the lake of Geneva, a phenomenon analogous to the mirage, but 
which, instead of being caused by horizontal reflection, was pro- 
duced laterally by the heating of vertical strata of air on the sides 
of mountains, which border on the lake where the phenomenon 
occurred. 

65. Those meteorological phenomena, called paraseline* and 
parhelion,| appear to be produced by reflection. When the moon 
rises after mid-day, and consequently at a time favourable to the 
appearance of the mirage, if the light of the sun and the clearness 
of the atmosphere allow the moon to be seen just as she gets above 
the horizon, two images of that satellite may be perceived. The 
parhelion is sometimes observed at sea, but it is a much more rare 
phenomenon than the preceding, depending, however, on a simi- 
lar cause. Among the instances recorded of the appearance of 
these mock suns may be mentioned the occurrence of four solai 
images observed at Rome in March, 1629, one being much tinted 
with the colours of the rainbow, and the others faintly coloured. 
Parhelia were seen by Cassini, in 1689; and they have also been 
noticed in England, Scotland, and America.^: 

66. On similar principles to those which serve to explain the 
mirage depend those appearances called looming, or the elevation 
of objects seen in the distant horizon above their usual level ; such 
as the Fata Morgana, observed in the Straits of Messina ; and the 
singular apparitions of ships and other objects in the air, some- 
times in a direct position, but more frequently inverted. 

67. The following figures are given from drawings of aerial 
spectra, observed at Dover, England, in May, 1833. When the 
real ship is visible, a double image may be formed, consisting of 
an inverted figure immediately over the ship itself, and another 

How is the constant retreat of the imaginary lake or river to be ex- 
plained. 

May any other than horizontal strata of heated air produce the effect of 
mirage ? 

What other phenomenon witnessed at sea is to be explained on the 
principles of atmospheric reflection ? 

* From the Greek preposition n* P *, with, and Zthw, the moon. 

t From n*p*, with, and h\«o>, the sun : i. e., appearing together with, 
or accompanying the sun. 

% For au account of the frequent appearance of parhelia, see Parry's 
account of his stay at Melville Island. — Ed. 
2 g 2 



354 optics. 

l'igure in an erect position, above the preceding. If there is a 
single figure only, it will usually be inverted with respect to the 
real ship below it. Sometimes a double image, or an erect figure 
with one below it inverted, will appear when the vessel thus re- 
flected is wholly invisible, or perhaps its topmasts be seen, while 
the remaining parts are hidden by the convexity of the earth's 
surface. 




68. The manner in which these and similar phenomena may 
be caused by reflection may be comprehended by reference to the 
analogous effect of spherical mirrors, subsequently noticed. But 
it is probable that, where double images of objects appear, the 
effect depends chiefly on the refraction of light, owing to the va- 
rying density of the atmosphere; and the circumstances under 
which such a state of the air may be produced have been pointed 
out and illustrated by Dr. Wollaston.* The refraction being 
greatest where the change of density is the most rapid, and less 
on each side of this point, the whole effect must be similar to that 
of a convex lens. 

69. In reference to the Fata Morgana, Dr. T. Young says, " It 
may frequently happen in a medium gradually varying, that a 
number of different rays of light may be inflected into angles equal 
to the angles of incidence, and in this respect the effect resembles 
reflection rather more than refraction."f 

Reflection from Convex Surfaces. 

70. The effect of light reflected from a convex mirror is to pro- 
duce a miniature picture of any objects placed opposite to it; the 
images thus formed appearing, to the eye of the observer in front, 

How will the appearance of spectre ships be affected by the nearness or 
emoteness of the real ships which cause the spectra ? 
How is refraction affected by change of density in the air ? 
What circumstance of the air may cause varying rays of incident light 
to be reflected to a focus ? 

What appearance is explained on this supposition ? 
What is the effect of reflection from a convex mirror ? 

* See a paper " On Double Images caused by Atmospheric Refrac- 
tion," in Philosophical Transactions for 1800. 
t Lectures on Natural Philosophv, vol. ii. 302. 



EFFECT OF CONVEX MIRRORS. 355 

to be situated within or behind the mirror. Thus the globular 
bottles rilled with coloured liquids in a chemist's shop-window 
present in pleasing variety the moving scenery of the street with- 
out; the upper hemisphere of each bottle exhibiting all the images 
inverted, while the lower displays a duplicate of them in an erect 
position. Hollow spheres of glass, covered on their interior su- 
perfices with an amalgam similar to that used for silvering look- 
ing-glasses, are sometimes suspended in apartments, where they 
present panoramic pictures of surrounding objects ; and convex 
mirrors are common articles of ornamental furniture exhibiting 
analogous phenomena. 

71. The images formed by reflection from a convex mirror must 
always be smaller than the objects by which they are produced, 
because the rays which form them become convergent in their 
passage to the eye of the observer. In the annexed figure let A B 
represent a convex mirror, the segment of a sphere, whose radius 

is the line G C ; and there- 
fore the point G will be the 
centre of the sphere, and the 
focus of the mirror. 

72. If an object be placed 
at E, at a great distance be- 
fore the mirror, its image 
will appear behind the mir- 
ror at a point near D, which 
will become the virtual fo- 
cus, and will be situated 
at half the length of the radius of the sphere, or at the middle 
point between the imaginary focus and the surface of the mirror ; 
and the magnitude of the image will be to that of the object in 
the ratio of the line C D to C E ; that is, it will be as much 
smaller than the object as the line C D is shorter than the line 
C E. 

73. If, therefore, the object be brought nearer to the surface of 
the mirror, the image also will approach to meet it, and become 
proportionally enlarged ; so that if a part of any object be brought 
into contact with the convex surface of the mirror, the image of 
that part will appear of precisely the same size as in the object 
itself: but unless the object be extremely small, or the mirror be 
a segment of a very large sphere, it must be obvious that only a 
small portion of an object can be made to touch the mirror, and 
hence the entire image must ever be to some extent inferior in size 
to the object by which it is produced. Not only will the rays 

How may bottles ofliquid and polished spheres produce doable images? 

What relation has the size of objects to that of their images in convex 
mirrors ? Explain the diagram. 

How far from the centre of curvature will an image formed by parallel 
rays of light falling on a spherical convex mirror appear to be situated ? 

What will be the effect of bringing the object nearer, so that rays may 
fall divergent? 




S\ 




356 optics. 

falling directly on the mirror, as E C, be reflected so as to form 
an image at D, but so likewise will any incident ray whatever, 
as E M, which will be reflected in the direction M N, so that the 
angle BMN will be equal to the angle C M E ;* and when the 
eye is at N, receiving the reflected ray M N, it will see the object 
E, according to that direction, and the image will appear in the 
mirror at D. 

74. A convex mirror by reflection converts parallel rays into 
divergent rays, those that fall on it in diverging lines are rendered 
still more divergent when reflected, and convergent rays are re- 
flected either parallel or less convergent. Suppose then an object 

A of some assignable mag- 
nitude A B, as repre- 
sented in the margin, to 
be placed before a con- 
vex mirror M N, the 
rays of light proceeding 
from each part of it will 
r ir be reflected as if from a 

single point, and an image will be formed as before, in the line 
drawn from each extremity of the object to the imaginary focus 
of the mirror F ; and in the same manner from other points, so as 
to form a complete image of the object. And this image must 
necessarily appear less than the object itself; for the rays which 
proceed from the extremity A will be reflected to the eye as if 
they proceeded from the point a, and those reflected from B as if 
from the point b, while the rays from the parts between A and B 
will be reflected from intermediate points ; and therefore the image 
must appear smaller than the object, by which it is produced. 

75. An object reflected from a convex mirror will not only form 
an image diminished in proportion but also defective in the outline ; 
for the virtual focus of reflection will vary for different parts of 
the same figure; therefore unless the object be relatively very 
small, or the curvature of the mirror very considerable, the central 
portion alone of the object will yield a correct image. Such at 
least will be the effect unless the curvature of the mirror be accu- 
rately formed, and expressly adapted to the purpose. The human 
eyeball constitutes an admirable convex mirror, reflecting minia- 

How may we conceive the incident rays on a convex mirror to be af- 
fected by an imaginary tangent plane at the point of incidence .' 

Flow will the rays reflected by a convex mirror be found in the three 
cases where they are respectively parallel, divergent and convergent be- 
fore incidence? 

Explain this by a diagram. 

* Every ray falling obliquely on the surface of a convex mirror may 
be regarded as impinging on a point which forms part of a plane tangen- 
tial to the curved surface of the mirror; and a line drawn perpendicular 
to such tangential plane will bisect the angle formed by the incident and 
the reflected ray, as is shown by the dotted lines in the preceding dia- 
gram. 



SINGULAR EFFECT OF A CHINESE MIRROR. 357 

ture images, the delicacy and beauty of which have repeatedly 
furnished topics of poetical allusion and metaphor. Here we 
perceive a striking instance of the vast superiority of the works 
of nature over those of art. 

76. A convex reflecting surface of variable curvature may afford 
many ludicrous caricatures of the human figure, or of that of any 
other animal, especially if the object be brought very near the 
mirror. That part of the surface which is most protuberant will 
exhibit a comparatively diminished image, and the effect will foe 
heightened by alternately advancing and withdrawing different 
parts of the person, and thus the disproportion between the head 
and the body or lower limbs may be rendered more remarkable. 
For if the head and trunk be thrown backward, while standing 
near the mirror, the image will display a diminutive head and 
body supported by preposterously swelled and gouty legs ; and 
on the contrary, if standing more backward, the body be bent with 
the head stretched out towards the mirror, it will present a mon- 
strous bloated figure with a dropsical head and body perched on 
spindle shanks. 

77. Sir David Brewster has published, in the Philosophical 
Magazine, an account of a curious convex metallic mirror, recently 
brought from China to Calcutta, the general appearance and effect 
of which is thus described : " This mirror has a circular form, 
and is about 5 inches in diameter. It has a knob in the centre of 
the back, by which it can be held, and on the rest of the back 
are stamped, in relief, certain circles with a kind of Grecian bor- 
der. Its polished face has that degree of convexity which gives 
an image of the face half its natural size ; and its remarkable pro- 
perty is, that ivhen you reflect the rays of the sun from the polished 
surface, the image of the ornamental border and circles, stamped upon 
the back, is seen distinctly reflected upon the wall." Mr. Swinton, 
the gentleman who transmitted from the East Indies the preceding 
statement of this apparent reflection of figures through an opaque 
substance, proposed a conjectural explanation of the strange phe- 
nomenon, as depending on the difference of density in different parts 
of the metal, occasioned by the stamping of the figures on the 
back, the light being reflected more or less strongly from parts 
that have been more or less compressed. 

78. But Sir D. Brewster, judging from the description, which 
alone had been transmitted to him, infers that " the spectrum in 
the luminous area is not an image of the figures on the back ; but 
that the figures are a copy of the picture which the artist has 
drawn on the surface of the mirror, and so concealed by polishing, 
that it is invisible in ordinary lights, and can be brought out only 
in the sun's rays." He had observed radiated lines and concen- 

What defect lias an image reflected by a convex mirror ? 
What natural convex mirror surpasses those produced by art ? 
What effect is obtained by convex surfaces of variable curvature ? 
How may the image of the person be caricatured by such an apparatus? 
What description and explanation are given of the Chinese mirror with 
figured back ? 



358 optics. 

trie circles to be similarly reflected by the light of the sun from po- 
lished steel buttons, which having been finished in a turning-lathe, 
the lines and rings had been formed on their surfaces by the ac- 
tion of the polishing powder or some similar cause, but too faintly 
to be visible except in the strongest light. Thus the figures on the 
back of the Chinese mirror were doubtless placed there merely to 
mislead the observer into a belief that he beheld them reflected 
through the metal, while he actually viewed the reflection of a 
duplicate of those figures lightly traced and concealed by the 
polish on the front surface. 

Reflection from Concave Surfaces. 

79. Concave mirrors exhibit a variety of phenomena depending 
on the situation of the object with respect to the mirror and to the 
observer, some of which are highly curious and interesting. " The 
concave mirror," says Sir David Brewster, " is the staple instru- 
ment of the magician's cabinet, and must always perform a prin- 
cipal part in all optical combinations."* Some of the most ex- 
traordinary optical effects in nature are also produced by reflection 
from concave surfaces, the properties of which therefore demand 
investigation. 

80. The manner in which light is reflected from concave mirrors 
may be thus explained : let A C B, in the marginal figure, repre- 
sent a mirror forming a 
part of a sphere whose 
centre is G, and G C, a 
radius; and suppose E 
to be an object far distant 
from" the mirror, then its 
image will appear in 
front of the mirror at D, 
the central point of the 

radial line C G. For any ray of light whatever, as E M, from 
the object E, falling on the surface of the mirror at the point M, 
will be reflected thence in such a manner as to pass through the 
point D ; and when the eye is placed at N, the object will be seen 
at or near D ; but this image will be to the object in the ratio of 
C D to M E, and consequently less than the object. If the ob- 
ject be made to approach nearer to the mirror, the image will re- 
cede from D towards G ; and if it be placed there, the object and 
image will coincide ; and the object still advancing from G, the 

In what manner does Brewster suppose the effect to have been pro- 
duced in that instrument ? 

How had Swinton previously explained it ? 

On what does the variety of appearances exhibited by the concave mir- 
ror depend ? 

Draw and explain a diagram by showing the manner in which light is 
reflected by a concave mirror. 

* Letters on Natural Magic, p. 61. 




B 



EFFECTS OF CONCAVE MIRRORS. 359 

image will retreat beyond it, till the object arrives at D, when the 
image will appear infinitely beyond E. B<ut if the object be placed 
yet further forward, between D and C, the image will fall behind 
the mirror, and it will look larger than the object. 

81. Thus it appears that when parallel rays fall on the ..surface 
of a concave mirror forming a portion of a sphere, they will be 
reflected and meet in a point at half the distance between the sur- 
face and tbe centre of concavity of the mirror. If the rays fall 
convergent on a concave mirror, they will be brought to a focus 
sooner than parallel rays ; and the focus will be nearer to the sur- 
face of the mirror than to the centre of concavity. When the 
rays fall in divergent lines, the focus to which they will be re 
fleeted will be more distant than that formed by parallel rays. 

82. There are three cases to be considered with regard to the 
effects of concave mirrors : 

1. When the object is placed between the mirror and the prin- 
cipal focus. 

2. When it is situated between its centre of concavity and that 
focus. 

3. When it is more remote than the centre of concavity. 

83. 1. In the first case, the rays of light diverging after reflec- 
tion, but in a less degree than before such reflection took place, 
the image will be larger than the object, and appear at a greater 
or smaller distance from the surface of the mirror, and behind it. 
The image in this case will be erect. 

84. 2. When the object is between the principal focus and the 
centre of the mirror, the apparent image will be behind the object, 
appearing very distant when the object is at or just beyond the . 
focus, and advancing towards it as it recedes towards the centre 
of concavity, where, as already stated, the image and the object 
will coincide. During this retreat of the object, the image will 
still be erect, because the rays belonging to each visible point will 
not intersect before they reach the eye. But in this ense, the 
image becomes less and less distinct, at the same time that the 
visual angle is increasing; so that at the centre, or rather a little 
before, the image becomes confused and imperfect; owing to the 
small parts of the object subtending angles too large for distinct 

What results in this case from the gradual approach of the objects to- 
wards the surface of the mirror ? 

What relation exists between the focal distance of parallel rays from a 
concave mirror and that of its centre of concavity ? 

Will convergent rays meet nearer to or further from the concave mirror 
than parallel ones ? 

How will the comparative distances of the foci of parallel and diver- 
gent rays be found ? 

State tbe three cases of parallel and divergent rays. 

What will be the relative size and distance of the object and tbe 
image in tbe first case ? 

Will tbe image be erect or inverted ? 

What will be tbe distance, positive and relative size of tbe image, in 
the second ~ ise ? 



360 optics. 

vision, just as happens when objects are viewed too near with the 
naked eye. 

85. 3. In the cases just considered, the images will appear 
erect; but in the case where the object is further from the mirror 
than its centre of concavity, the image will be inverted; and the 
more distant the object is from the centre, the less will be its 
image, and the further from the said centre, or the nearer the focus, 
and the converse ; the image and object coinciding when the latter 
is stationed exactly at the centre, as noticed in the preceding case. 

86. If an observer view his own image at a considerable dis- 
tance beyond the centre of a concave mirror, the image will ap- 
pear small, faint, and somewhat confused. This is owing to the 
smallness of the number of rays that can enter the eye ; hence 
the apparent distance is augmented or rendered uncertain, so that 
the image is conceived to be beyond or within the mirror, and this 
misconcep-tion increases the confusion. As the observer advances 
towards the mirror, his image will gradually appear larger and 
brighter, and likewise draw nearer to him ; but if he do not view it 
between himself and the mirror, it will continue still indistinct. At 
length he will arrive at the station whence the image assumes a de- 
terminate and correct figure, appearing perfectly distinct. After a 
few trials, the true place for viewing the image may be ascertained 
with tolerable accuracy ; and it will continue distinctly perceptible 
when the observer moves a short distance backwards or forwards 
from the proper position : but advancing beyond it, the image will 
soon begin to appear indistinct, and this indistinctness will in- 
crease till he arrives so near the mirror as its centre of concavity, 
where the image will be lost in confusion. If he still advances, 
another image in an upright position gradually becomes visible, 
as explained in the preceding case. 

87. The most singular and curious effects of concave mirrors 
are those resulting from the position of objects at a greater dis- 
tance^rom the mirror than its centre of concavity, as in the third 
case above described, when a diminished and inverted image will 
be formed in the air between the object and the mirror. In order 
that this may be seen to the utmost advantage, particular situa- 
tions must be assigned both to the object and the observer, which 
will be regulated by the concavity of the mirror and its consequent 
focal distance. For the exhibition of such phenomena, however, 
spherical concave mirrors are not so well adapted as those of an 
elliptical figure, for the latter having double foci, any object placed 
in one focus of an elliptic concave mirror will form an accurate 
image in the other focus. 

How will these three things be found related to each other in the third 
case ? , 

Why is the image of a distant observer seen indistinctly in a concave 
mirror ? 

Which case of reflection by concave mirrors produces the most inter- 
esting phenomena ? 

What form of concavity ought the mirrors to possess for the exhibition 
of these phenomena ? 



OPTICAL DECEPTIONS. 



361 




88. The marginal 
figure exhibits a con- 
venient mode of ar- 
rangement for pro- 
ducing optical images 
in the air by means 
of a single mirror.-}- 
Suppose C D to be 
one side of a room, or 
a screen dividing one 
part of the room from 
another, and having 
iu it a square aperture E F, the centre of which may be about five 
feet above the floor. This opening may be surrounded with a 
black border, or a gilt moulding, so as to resemble a picture-frame. 
A large concave (elliptical) mirror, M N, is then to be placed in 
?„n adjoining apartment, so that when any object is placed at A, 
in one focus of the mirror, a distinct image of it may be formed in 
the other focus at B, or in the centre of the^erture E F. This 
image will be inverted with respect to th2 position of the object; 
therefore if a small statue, bust, or plaster cast of any object be 
placed upside down at A, an observer in the apartment at O will 
behold an erect image of the object at B. In order to give the 
greater effect to this exhibition, the object should be white, or at 
least of a very bright colour, and should be strongly illuminated 
by a powerful lamp, the rays of which must be prevented from 
reaching the opening E F. 

89. In this case, the image being formed, not in the single fo- 
cus of a spherical concave mirror, but in one of the foci of an ellip- 
tical mirror, it will not be confused or reduced; but will be rather 
.arger than the object. When the image appears in the air, as 
here described, it will be distinctly visible only from the point 
0, and a person placed at a little distance, on either side, will see 
nothing of it. If, however, the opening E F be filled with smoke, 
rising from burning frankincense or other perfumes, the cloudy 
vapour will serve as a screen to receive the reflected image, which 
may thus be rendered generally visible to persons within the 
room 0. 

90. Among the natural phenomena which appear to be caused 
by reflection from concave surfaces may be mentioned what is 
called in Germany the "Spectre of the Brocken," a gigantic figure 
sometimes seen at a distance upon the highest peak of the Harz 
Mountains, in the kingdom of Hanover. It has been ascertained, 
from, careful observation, that the figure is a reflected spectrum oi 



Describe the arrangement of apparatus tor exhibiting aerial images.. 

Will the images in this case be direct or inverted ? 

What will be the size and position of the image, with regard to those 
of the object ? 

How are reflections from ooncave surfaces applied to explain the spec- 
tre of the Brocken > 

2H 



362 optics. 

the observer, such as might be produced in certain situations by 
means of a concave mirror. A singular instance of atmospheric 
reflection, as observed in Sicily, from Mount Etna, has been no- 
ticed by a modern traveller. He says, "At the extremity of the 
vast shadow which Etna projects across the island, appeared a 
perfect and distinct image of the mountain itself, elevated above 
the horizon, and diminished, as if viewed in a concave mirror."* 
91 . Various forms may be given to mirrors besides those already 
described, and thus various modifications of the reflected images 
may be produced. Cylindrical, conical, pyramid ical and prismatic 
mirrors are sometimes constructed, but they merely serve the pur- 
pose of creating amusement, by the singularity of the effects 
which may be exhibited by means of such instruments. A com- 
mon method of displaying these optical phenomena consists in the 
rectification of distorted figures (drawn for the purpose,) by re- 
flection from certain mirrors. These exhibitions are termed Ana- 
morphoses ;| and the rules for delineating deformed figures to suit 
the different kinds of mirrors, with directions for their proper ar- 
rangement, may be found in several works relating to optical in- 
struments and phenomena.:}: 



DIOPTRICS. 



92. Rays of light in passing to any distance through a medium 
of uniform density will proceed in right lines ; but if a ray or pen- 
cil of rays be made to pass from one transparent medium to ano- 
ther, as from air into water or glass, its direction will be changed 
at the surface of the new medium, and it will afterwards proceed 
in a line varying more or less from that in which it passed through 
the air. Hence a ray is said to be refracted or bent, in conse- 
quence of its transit from one medium to another ; the effect pro- 
duced is termed refraction of light; and the laws by which the 

To what use have cylindrical mirrors been chiefly applied ? 

By what name are the changes of figure produced by curved mirrors 
designated ? 

What difference exists between the course of a ray of light while tra- 
versing a uniform, and that which occurs while passing through a variable 
medium ? 

What is meant by refraction of light? 

To what division of optics does this effect give rise ? 

* Travels in Sicily, Greece, and Albania. By the Rev. T. S. Hughes, 
1830. 

t From the Greek preposition Av*, and Mo f ?coo-<s, an appearance : i. e, 
a reversed exhibition. 

$ V. Schotti Magia Universalis, p. i. lib. 3. ; P. Dubreuil Perspective 
Pratique, t. iii. Trait. 5, 6, 7 ; Wiegleb's Natural Magic, (German) ; and 
Hutton's Recreations in Nat. Phil. vol. iii. 



REFRACTION OF LIGHT. 363 

phenomena are regulated constitute the science, or branch of sci- 
ence, called Dioptrics.* 

93. The effect just described may be easily subjected to obser- 
vation, by laying - a piece of money near the centre of the bottom 
of a china bowl, or basin, placed on a table or on the floor, and x > 
then retreating backward till the money is no longer visible, being 
hidden from the eye by the side of the bowl : if then water be 
poured into the vessel, the piece of money will become visible, just 
as if the bottom of the basin was raised above its real level. As 
this experiment may be readily repeated, and affords a convincing 
proof of the position above stated, it may be proper to observe that 
the money, or any other flat object which will equally well answer 
the purpose, should be fastened to the bottom of the basin with 
sealingwax, that it may not be moved from its place when the 
water is poured on it, and that the vessel must be filled to a cer- 
tain height before the object can be seen. 

94. The refraction of light may be exhibited more simply by 
plunging a straight cane or long ruler obliquely into a pond or 

a bucket of water, when it will appear bent at the surface of the ' 
water; that part of the cane held by the hand in the air appearing 
to be joined at an obtuse angle to the part under water. 

95. There is, however, one case in which rays of light, in their 
passage from one medium to another of different density, will pro- 
ceed without changing their direction ; and that is when their di- 
rection is perpendicular to the connecting surfaces of the two 
mediums. Thus, if the eye be placed vertically above a piece of /" 
money in a basin, it will be seen in the same vertical line whethei 
the basin be empty or filled with water; and for the same reason 

a straight stick held perpendicularly in water will not assume the 
bent figure which may be remarked when it is held obliquely. 

96. If, from the point where a ray of light passes from one me- 
dium through the surface of another medium, we conceive a line 
to be drawn perpendicular to that surface, and prolonged indefi- 
nitely beyond it, the ray after refraction will either approach the 
perpendicular more than before refraction, or recede further from 
it than before. If the medium which the ray enters be more dense 
than that which it quits, it will approach the perpendicular; but 
if the second medium be rarer than the first, the contrary effect 
will take place, and the ray will recede from the perpendicular. 

What simple experiment illustrates the effect of refraction ? 

What precaution is required to insure its success ? 

Why does a stick appear bent when plunged obliquely into the water ? 

Under what condition does change of density in the medium produce 
no change of direction ? 

What course will the incident and the refracted rays respectively take 
with reference to a perpendicular to the refracting surface ? 

Distinguish the case where the ray enters a rarer from that in which it 
enters a denser medium. 

* From the Greek A*057"ro,u;*»,to see through; or A.orrT ? s,a mathemati- 
cal instrument for measuring heights. 



364 



OPTICS. 




97. These effects may be illustrated 
by means of the marginal figure. Sup- 
pose O to be the point at which the lu- 
minous ray passes from one medium to 
another, and that the two are separated 
by the line B D, representing any sur- 
face either plane, concave, or convex; 
suppose the medium above BD to be 
more rare than that below it, and let 
H O represent the incident raj r , and O C 
the refracted ray, and draw through the 
point 0, I F perpendicular to the plane B D ; then if the ray H O 
had preserved its direction after passing the plane, the angles 
HOI and F O C must have been equal ; but the latter is more 
acute than the former, because the line of refraction O C ap- 
proaches more to the perpendicular I F than the line of incidence 
HO. On the contrary, if the medium below B D had been rarer 
than that above it, the ray would have been less refracted than 
before, and would consequently have diverged further from the 
perpendicular I F than the ray H does, and would therefore 
have formed an angle F O A more obtuse than HOI. From the 
point as a centre describe the circle I D F B, cutting the direc- 
tions of the incident and the refracted ray in the points H and C ; 
from those points draw the lines H N and C R perpendicular to 
I F, which lines will be the sines of the angles HOI and F O C. 

98. It has been ascertained from numerous observations that 
these lines are always in the same ratio, whatever be the angle of 
incidence at which the ray falls, provided the mediums through 
which it passes remain the same ; for though there is no fixed re- 
lation between the angle of incidence and the angle of refraction, 
there is always a certain proportion between the sines of those 
angles. H N is called the sine of the angle of incidence, and 
C R the sine of the angle of refraction. 

99. When a ray passes from air into glass, the sine of its angle 
of incidence will be to that of the angle of refraction, in the ratio 
of 3 to 2 ; if it passes from air into water, the ratio of the sines 
will be as 4 to 3 ; but these ratios will be inverted when light 
passes from glass or water into air; for in the former case the 
ratio of the sines will be as 2 to 3, and in the latter as 3 to 4. 
These ratios, as just noticed, are constant, whatever be the angle 
of incidence, for the respective mediums. But they differ con- 
siderably for different substances ; and the refractive powers of a 

Draw and explain the diagram relating to refraction. 

To what trigonometrical lines are the refractive powers of bodies com- 
parable ? 

What line on your diagram is the sine of the angle of incidence? 

Which is the sine of the angle of refraction ? 

What relation will exist between these two sines when light passes from 
air into glass ? from air into water ? 

What will be their ratio when li°-ht oasses from glass and from water 
respectively into air ? 



ATMOSPHERIC REFRACTION, 



365 



considerable number of bodies have been ascertained by experi- 
ment.* 

100. No general principle has been discovered which connects 
the refractive power of bodies with their other physical properties ; 
though it is usually highest in the densest transparent substances, 
and in such as are of an inflammable nature. Sir Isaac Newton 
having observed that several inflammable bodies possessed high 
refracting powers, and noticing a similar property in the diamond, 
ingeniously conjectured that gem to be an inflammable substance, 
long before its composition was known ; and analysis has verified 
his idea, and shown it to consist of crystallized carbon. 

101. As the effect of any transparent medium, in the refraction 
of light, generally increases with increase of density, so air and 
vapours when dense display greater power of refraction than when 
comparatively rare ; and hence some curious and important phe- 
nomena depend on atmospheric refraction. 

102. Light, on entering the atmosphere of the earth, encounters 
a medium less rare than the more ethereal space beyond it, and as 
the lower portion of the atmosphere is relatively the densest, rays 
passing through the air from objects far above us must be con- 
siderably refracted. From this cause the sun and other celestial 
bodies are never seen in their true situations, unless they happen 
to be vertical ; and the nearer they are to the horizon, the greater 
will be the influence of refraction in altering the apparent place 
of any of those luminaries. 




What relation have the refracting powers to the other physical proper- 
ties of bodies ? 

What effect on refracting- power has the increase of density ? 

What atmospheric phenomena depend on this refractive influence? 

Explain by diagram the effect of refraction on the apparent place of the 
heavenly bodies. 

* The quotient found by dividing the sine of incidence by the sine of 
refraction is called, by optical writers, the index of refraction ; and, as 
stated in the text, different bodies having different refractive powers will 
present different indices. The following are a few of the substances of 
which these indices have been experimentally determined : 
Diamond 
Melted sulphur . 
Glass, 2 lead, 1 flint, 
Oil of Cassia 
Quartz 



2.439 


Amber 


1.547 


Water 


1.336 


2.148 


Oil of Turpentine 


1.475 


Tee 


1.309 


1.830 


Olive Oil . 


1.470 


Ether . 


1.057 


1.641 


Alum 


1.457 


Air 


1.000294 


1.548 


Alcohol 

2h2 


1.372 




[Ed. 



366 optics. 

103. Thus a spectator at A, in the annexed figure, would see 
the sun rise at C, when its real situation was at S ; and so its ap- 
parent place would be relatively altered till it arrived at the zenith 
vertically above the point A; but it can be so situated only with 
respect to observers under the equator, or at least in the torrid zone. 
In consequence of this atmospheric retraction the sun sheds his 
light on us earlier in the morning and later in the evening than we 
should otherwise perceive it. And when the sun is actually be- 
low the horizon, those rays which would else be dissipated through 
space are refracted by the atmosphere towards the surface of the 
earth, causing twilight. The greater the density of the air, the 
higher is its refractive power, and consequently the longer the du- 
ration of twilight. 

104. In cold climates, as near the poles, where the year is 
naturally divided into seasons of light and darkness, each lasting 
six months, the twilight of the circumpolar atmosphere diminishes 
the winter-night of those gloomy regions by a period equal to 
several days. Hence also terrestrial objects, viewed at a great 
distance, are afiected by atmospheric refraction ; and they there- 
fore appear more elevated and nearer to the observer than they 
would if seen through a medium of uniform density. 

105. Those optical phenomena depending on refraction, with 
which we are most familiarly acquainted, are such as are produced 
by the passage of rays of light from any medium, as air or water, 
into another more or less dense, and their entering again the for- 
mer medium after they have traversed the more or less refracting 
medium. Thus objects seen through a common reading-glass or 
a pair of spectacles, if observed at certain distances, will be in 
some degree magnified ; and glasses used by short-sighted per- 
sons have the effect of reducing the size of objects seen through 
them. And when any transparent substance is held between the 
eye and any object, the rays which render that object visible will 
be refracted in their passage from the air through the transparent 
substance, into the air again, before they reach the eye ; and the 
effect produced will depend on the refractive power of that sub- 
stance, and the figure of its surfaces. 

106. The most simple case of this na- 
ture is when the denser or more refract- 
ing substance is terminated by plane sur- 
faces parallel to each other. Suppose 
A B to be a section of a plate of polished 
glass, terminated by parallel surfaces 
I ?', on which falls obliquely the ray 
DC at the point C, it will be refract- 
ed on entering the glass, and its direc- 

How is the duration of twilight affected by the density of the air ? 
What benefit do the polar regions derive from the refractive power of 




air 



What effect on the apparent position of objects, on the surface oJ the 
«arth, is produced by refraction ? 




EFFECTS OF TRANSPARENT PLATES. 367 

tion will be changed so as to approach nearer to a perpen- 
dicular to the plane of the glass, passing through it in the line C c; 
but on emerging at c it will be again refracted in the contrary 
direction, and will proceed in the line c d, parallel to DC d'. 
Thus rays being restored to their former direction after being re- 
fracted through°plates of glass, or other transparent bodies with 
parallel surfaces, the effect is not perceptible ; and hence the forms 
and situations of objects are not affected by viewing them through 
the panes of a glass window. 

107. When the plane surfaces of a transparent substance are 
not parallel to each other, different effects will be produced. Let 

X represent a section of a medium denser than that 
surrounding it, and terminated by inclined planes, 
across which pass rays of light, from the point O. 
Then the ray O b will be refracted in the direction 
b b', and after emerging, it will pass in the line b' o ; 
another ray O a, from the same luminous point 0, 
will in the same manner be refracted from a to a', 
and meet the former ray in the point o. If an eye 
be supposed to be placed at o, the luminous point O 
will be doubled ; one image being formed by rays 
O passing through the surface Z>, and another by those 

passing through the surface a. 

108. If, instead of a and b only, there were three, four, or any 
greater number of plane surfaces, the eye at o would perceive a 
light or other object at 0, multiplied as many times as the num- 
ber of facets into which the sides a b were thus divided. Hence 
also when glass is furrowed into a multiplicity of minute surfaces 
by grinding, the rays of light in passing through it are refracted 
as from innumerable small facets, and therefore objects are not per- 
ceived at all through it ; for, if the images of them were formed 
in proper directions, they would be too diminutive to be visible. 
Such glass, forming a transparent screen, is sometimes used in 
the windows of offices and counting-houses, as the light passing 
through them is more generally diffused, and the shadows are very 
faint ; and for these reasons, circular screens of ground glass are 
adapted to lamps, hence called sinumbral* lamps. 

109. Glass and transparent crystals, but chiefly the former, are 
the substances generally employed in the construction of optical 
instruments for exhibiting the phenomena depending on the refrac- 
tion of light ; and having noticed the effects produced by transpa- 

State some of the familiar optical phenomena depending on refraction 
How are rays of light affected on entering obliquely and passing through 
a plate of glass with parallel surfaces ? 
Explain this by a diagram. 

How will the effect be varied where the surfaces are not parallel ? 
What effect would result from multiplying the surfaces of incidence ? 
Why does a furrowed or ground surface not give distinct images? 
Of what utility is the indistinctness produced by roughened glass f 

* From the Latin sine, without, and umbra, a shadow. 



^68 



OPTICS. 



rent bodies with plane surfaces, we shall now proceed to investi- 
gate the properties of glasses with curved surfaces. There are 
numerous varieties of such glasses, usually termed optical lenses ; 
but they may all be arranged in two classes : (1.) convex lenses, 
or those which are thicker in the centre than towards their borders ; 
(2.) concave lenses, or glasses thinnest in the centre. 

E 




110. Among convex lenses are the double convex, A, to which 
the appellation, lens, was originally applied, from its resemblance 
to a lentil-seed {lens, in Latin), being bounded by two convex 
spherical surfaces, whose centres are on opposite sides of the lens ; 
the plano-convex, B, having one side bounded by a plane surface, 
and the other by a convex surface ; and the meniscus, or concavo- 
convex, C, bounded on one side by a concave, and on the other 
by a convex surface ; the former being a portion of a larger circle 
than the latter, and therefore the surfaces meet, when produced. 

111. There are also three principal varieties of concave glasses ; 
as the double concave, D, bounded by two concave surfaces, form- 
ing portions of spheres whose centres are on opposite sides of the 
lens; the plano-concave, E, bounded on one side by a plane, and 
on the other, by a concave surface ; and the convexo-concave, F, 
bounded by a convex surface on one side, and by a concave one 
on the other, but these surfaces when produced do not meet. 

112. The varieties of both classes of lenses admit of numerous 
modifications depending on the relative curvature of their several 
surfaces. The radius of a lens will be the radius of the sphere 
of which its surfaces form a part, if both surfaces have the 
same curvature ; but otherwise each side will have a different ra- 
dius. In all the various kinds of lenses there must be a point 
where the opposite surfaces are parallel ; this point is termed the 
optical centre of the lens, and a line passing through it perpendi- 
cularly to the surface will be its axis. On this line will be situ- 
ated the geometrical centres of the two surfaces of the lens, or 
rather of the spheres of which they form portions. A lens is said 
to be truly or exactly centred when its optical centre is situated 



Into how many classes may lenses be divided ? 
How are they distinguished ? 

What names are given to the different varieties of convex lenses t 
What to the three forms of concave lenses ? 

According to what circumstances in their construction do these forms 
vary in different glasses ? 

What is meant by the optical centre of a lens ? 
What line forms the axis of a lens ? 
When is a lens considered exaetly centred ? 



EFFECTS OF CONVEX LENSES. 



369 




at a point on the axis equally distant from corresponding parts of 
the surface in every direction ; as then objects seen through the 
lens will not appear altered in position when it is turned round 
perpendicularly to its axis. 

113. The general effect of those glasses which are styled con- 
vex lenses, or which are thickest in the centre, is to render rays 
which pass through them more convergent ; and that of concave 
lenses, on the contrary, to render rays more divergent. The man- 
ner in which light is refracted by a convex lens may be illustrated 
by means of the annexed figure. 

114. Suppose A B to 
be a double convex lens, 
the axis of which is D'C 
G', and C its optical cen*- 
tre, then the parallel rays 
D A, D" B, will be so re- 
fracted at the two sur- 
faces as to meet at G', 
which point is termed 
the "principal focus" of 
the lens. And the pa- 
rallel rays E A, E' C, and 
E"B, andalsoF,A,F'C, 
and F" B, falling obliquely on the lens, will in a similar manner 
be refracted, and have their foci at G and G", at the same dis- 
tance behind the lens. 

115. It may be observed that the rays E' C G", D' C G',F' C G, 
passing through the centre of the lens, do not alter their direction. 
C G' is termed the " focal distance" of the lens ; and in a double 
convex lens, formed of equal spherical surfaces, its length will be 
that of the radius of the sphere of which those surfaces form por- 
tions. In a plano-convex lens the focal distance will be equal to 
double the length of the radius of its curved surface. If the lens 
be unequally convex, the focal distance may be found by multi- 
plying together the radii of its two surfaces, and dividing the pro- 
duct by the sum of the two radii, the quotient being the focal dis- 
tance required. 

116. When converging rays, or those proceeding towards one 
point, as D A G, E C G, and F B G, fall on the surface of a con- 
vex lens A B, the principal focus of which is at 0, they will be- 

What test may be adopted of the accuracy of such centring ? 
What is the effect of convex and concave lenses respectively ? 
Illustrate the manner that parallel rays are refracted by a convex lens ? 
What is meant by the principal focus of such a lens ? 
What is meant by the focal distance? 

How may this distance be known in spherical lenses of unequal con- 
vexity ? 

What will it be in a plano-convex lens ? 

How can it be found in lenses having curves unequally convex ? 

How does a convex lens affect converging rays ? 



370 



OPTICS. 




come more convergent, and 
will therefore be refracted to 
a focus at H, nearer the lens 
than the point 0. The more 
a distant may be the point a, at 
which the rays would meet if 
uninterrupted, the further will 
the point H recede from the 
surface of the lens towards 0, 
beyond which point it never goes ; and the nearer the point a to 
Ihe lens, the nearer will the point H advance towards it. 

117. The points G and Hare named "conjugate foci," because 
the place of one depends on that of the other, and though every 
lens has only one principal focus, it may have an indefinite num- 
ber of conjugate foci, as rays may fall on it converging at innu- 
merable angles. The conjugate focal distance, C H, may be 
found by multiplying the principal focal distance, O C, by a C, 
the distance of the point of convergence, and dividing that product 
by the sum of the same numbers, when the quotient will give the 
distance required C H. 




118. When diverging rays, or those issuing from one point, as 
E A, and E B, fall on a convex lens A B, the principal focus of 
which is at O, the refractive power of the lens will make them 
converge to a focus at G, beyond 0. As the point whence the 
rays diverge recedes from the lens, the focus G will advance to- 
wards it, and when the point of divergence E is infinitely distant, 
the point G will coincide with the principal focus O, for rays 
issuing from a point at an infinite distance must be virtually pa- 
rallel rays. If E approaches to O', the focus G will recede from 
O, and when E coincides with 0', G will be infinitely distant, or 

What are meant by the " conjugate foci" of a lens ? 

How is the conjugate focal distance for converging rays found ? 

In what position, with respect to the principal focus, will the conjugate 
focus of diverging rays be situated ? 

What effect will the indefinite distance of the point of divergence pro- 
duce on the position of their focus ? 

With what point will it then coincide ? 

How may rays after refraction by a convex lens become parallel ? 

Where must the point of divergence be situated in order that they 
should be divergent after refraction ? 



EFFECTS OF CONVEX LENSES. 



371 




the rays will become parallel after refraction. And when F is be- 
tween O' and C, as at H, the refracted rays will become diver- 
gent, as A L, B K, as if they had proceeded from a focus I, be- 
yond O' and in front of the lens. The points E and G are termed 
the conjugate foci, as before; and the conjugate focal distance 
may be found by multiplying the principal focal distance by E C, 
the distance of the point of divergence from the lens, and dividing 
the product by the difference of those numbers, and the quotient 
will be the required distance C G. 

^ 119. Rays of light passing 
through concave lenses will, in 
most cases, be rendered more 
divergent by refraction, what- 
~ e ever be their previous direction. 
Suppose A B to be a double 
concave lens, whose axis is E C 
^ /. e, and C, its optical centre ; then 
the parallel rays D A, F B, 
falling on it, will be refracted into the lines A d, B /, as if they 
diverged from a point O, before the lens, which is its principal fo- 
cus. The principal focal distance is relatively the same as in a con- 
vex lens, and may be ascertained in the same manner, whether 
the sides be of equal or unequal curvature. 

120. When con- 
-& verging rays D A, 
F B, proceeding to 
a point G, beyond 
the principal focus 
O of a concave lens, 
fall on it, they will 
be refracted into the 
diverging lines A d, 
and B /, as if they 
issued from a focus H in front of the lens beyond O'. When G, 
the point of convergence, coincides with O, the rays will be pa- 
rallel after refraction ; and when the point G falls within the point 
O, the refracted rays will converge to a focus on the same side of 
the lens with G, but on the other side 0. G and H are styled 
conjugate foci, and the situation of one of them, when the other is 
known, may be found by the rule given in the case of converging 
rays falling on convex lenses. 




What directions will rays generally follow after refraction by a con- 
cave lens ? 

Where is the principal focus of such a lens conceived to be situated ? 
- In what manner will the principal focal distance be ascertained ? 

How will converging rays be refracted, which, before refraction, con- 
verge to a point beyond the principal focus ? 

In what manner will they be refracted if converging directly towards 
the principal focus ? 



372 



OPTICS. 




121. When diverging rays 
D A, F B, from any point F 
beyond the focus 0' fall on a 
concave lens A B, they will 
diverge in the directions A d, 
B/, as if proceeding from a 
point H, between O' and C ; 
and as F advances towards C, 
so will H likewise : that is, 
the more divergent the rays are 
before refraction the more will 
they diverge afterwards. When 
the distance F C or H C is given, the other point may be found 
by the rule for diverging rays falling on convex lenses. 

122. Meniscus, or concavo-convex lenses, have the same effect 
on rays of light as convex lenses corresponding with them in focal 
distance. Convexo-concave lenses have the same effect as con- 
cave lenses agreeing with them in focal distance. 

123. The manner in which images are formed by means of op- 
tical lenses may be readily conceived from the preceding figures 

and descriptions; and the ef- 
fect of convex glasses, in mag- 
nifying the images of objects, 
may be further elucidated by 
reference to the annexed dia- 
gram. Let A B represent a 
convex lens, of which C d is 
the optical axis ; and let E F 
be any object to be examined, 
placed between the principal 
focus and the surface of the lens ; then a ray E g falling on the 
lens parallel to its axis will be refracted in the direction g C, and 
another ray E G H, from the same point, falling obliquely on the 
lens and passing through its optical axis, will be continued in the 
same direction without being affected by refraction, and the two 
rays will become more divergent after passing through the lens ; 
whence it follows that if the ray E G H were prolonged beyond 
E, it would cut the line g e in the point e, and an eye placed be- 
hind the lens would see the extremity E of the object at e; and 
rays proceeding from every other part of the object being refracted 
in a corresponding manner, the image of the object E F will ap- 
pear as at ef, and therefore be larger than the object. 

What will be the directions after refraction of rays diverging from a 
point beyond the principal focus of a concave lens ? 

Can diverging rays ever become either parallel or convergent by the 
refraction of such a lens ? Why ? 

What two rules apply for finding the focal distances of Meniscus lenses ? 

Draw and explain a diagram to illustrate the magnifying effect of con- 
vex lenses. 

What effect is produced by refraction on rays passing through the op- 
tical axis of a convex lens ? 




DESCRIPTION OF THE EYE. 373 

124. But if the object be placed at the focus of the lens, the 
rays refracted being chiefly such as were parallel to its axis before 
refraction, the eye will not perceive a distinct image of the object. 
If we suppose the object E F to be placed beyond the focal dis- 
tance, the rays E g, E G, from the same point E will become 
convergent after having traversed the lens, and will intersect each 
other below the axis, E G as passing through the centre of the 
lens not having its direction altered by refraction ; all the rays 
from different points of the object will take analogous directions, 
and thus there will be formed on the opposite side of the lens a 
reversed image of the object. And if the lens be fixed in an aper- 
ture in a window-shutter, and all light but what passes through 
it be excluded, the image may be rendered visible, by placing a 
sheet of white paper opposite the aperture to receive it. A room 
thus fitted up would be literally a camera obscura, a darkened 
chamber. 

The Organs of Vision. 

125. The eyes of animals bear a certain analogy to the optical 
instrument called a camera obscura, just mentioned; for the ima- 
ges of external objects, within the sphere of vision, are actually 
formed or traced within the eye, in the manner that will be sub- 
sequently described. 

126. In man and other animals destined to inhabit the surface 
of the earth, the eyeball is a mass nearly spherical, but somewhat, 
flattened in front. Those animals that dwell in the water have 
eyes very much flattened, the eyeball in most fishes forming but 
half a sphere, and in the ray species, it is but one quarter of the 
thickness of a sphere. In those birds that soar to the higher re- 
gions of the atmosphere, the anterior part of the eye is sometimes 
flat, and sometimes in the figure of a truncated cone : the upper part 
forming a short cylinder, surmounted by a very convex eminence. 

127. The eyes of spiders, scorpions, &c, are merely very mi- 
nute points, which it would be difficult to recognise as organs of 
vision, if their functions had not been demonstrated by precise 
experiments. Millepedes, flies, &c, have eyes often very large 
in proportion to the bulk of the insect, and composed of a multi- 
tude of small facets, or plano-convex lenses united into a hemi- 
spherical form, with their axes directed to a common focus. 
Many insects have, at the same time, simple and compound eyes : 
this is the case with wasps, grasshoppers, and some others. There 

Why does the eye not perceive a distinct image of an object at the 
principal focus of a convex lens ? 

In what position will the image appear when the object is beyond the 
principal focus ? Explain the cause of this on the diagram. 

In what manner may this position of the image be verified ? 

What is a camera obscura? 

To what is the construction of the eye analogous? 

What relative sphericity have the eyes of land and of aquatic animals' 

What peculiarity is found in the eyes of birds that soar to great 
heights ? What, in those of spiders and scorpions ? 

2 I 



374 



OPTICS. 




exist likewise multitudes of animals, in which no organ of vision can 
be discovered ; but it appears, thatin such the sense of feeling is ex- 
tremely delicate, and therefore supplies the defect of the other senses. .. 
128. In the following descriptive notices of the organs of vision, 
and the phenomena depending on them, our attention will be restric- 
ted to the structure and functions of the human eye. But the eyes 
of some quadrupeds, as the ox or the sheep, so far resemble those 
of man, that sufficiently accurate ideas of the essential parts of 
the eye may be obtained by dissecting and examining an eye of 
either of those animals, and comparing its mechanism with the 
ensuing description. 

129. The annexed figure exhibits a front 
view of the eye, or the anterior portion 
of the eyeball. The white part surround- 
ing the centre is called the sclerotic* coat 
[tunica sclerotica), a o, and it is continued 
within the orbit, round the back part of 
the eyeball, being formed of a dense mem- 
brane, which includes, as in a bag, the 
other parts of the eye. It is perfectly 
opaque, and therefore is not continued over the front of the eye, 
but joins the transparent cornea, ] b, which differs from it chiefly 
in being completely pervious to light, and therefore serves like a 
window to admit it to the interior of the eye for the formation of 
images. Within or behind the cornea may be perceived the iris,:£ 
c, a sort of coloured fringe, usually either of a dark brown or a 
grayish-blue tint ; and hence the distinction between black, and 
blue or gray eyes : but there are persons with extremely light 
complexions and white hair (Albinos), who have red eyes, the 
iris being red, as in the eyes of a white rabit. In the centre of 
the eye, surrounded by the iris, is a dark circular space of variable 
dimensions, called the pupil, d, through which the rays of light 
pass into the chambers of the eye. 

130. An horizontal section of the 
eye is represented in the marginal 
figure, in which the parts already 
described are shown, as well as 
those of the interior. It will be 
perceived that the eye is enveloped 
in four membranes or tunics, the 
sclerotic coat, AAA; the cornea, 
or horny coat, B B, connected with 
the former, in the front of the eye; 
the choroid coat,§ T T, which 
forms a lining to the sclerotic coat, 
and on its opposite surface is co- 

* From the Greek rxv-ipoc, hard, firm ; or, ZxA^po-ri!,-, hardness. 

t From the Latin corneus, horny, or like horn. 

$ So called from its being like the rainbow (iris), variously coloured. 

§ From its resemblance to another membrane called, in Greek, Xcp.ov. 




THEORY OF VISION. 375 

vered by a black pigment (pigmentum nigrum), on which lies the 
interior coat of the eye, called the retina,* RR, a delicate reticu- 
lar membrane, expanded over the posterior chamber of the eye, 
and proceeding from the optic nerve, 0, by which sensations are 
conveyed to the brain. 

131. The interior of the eye, or the cavity surrounded by the 
coats just described, is filled by three substances called humours : 
the first, or the aqueous humour, D, is a fluid situated immediately 
behind the transparent cornea, and chiefly in front of the iris ; the 
second in situation is the crystalline humour, C, directly behind 
the iris, being a solid, transparent lens, more convex behind than 
before ; and the third is termed the vitreous humour, V, a kind of 
viscous solid mass, of a medium consistence compared with the 
other two, occupying the posterior chamber of the eye, supporting 
the other parts, and contributing chiefly to preserve the globular 
figure of the eye. Between C and D is the pupil or opening in the 
iris, 1 1, through which light is admitted into the eye ; and behind 
the iris the crystalline humour or lens is suspended in a transpa- 
rent capsule, by the ciliary processes, L L, which proceed from 
the iris. 

132. The eyes are situated in basin-shaped cavities in the skull, 
called the orbits, and there are various muscles attached to the 
ball of the eye and to different parts of each orbit, which by their 
contraction give a certain degree of lateral or rolling motion to 
the eye, and thus assist in directing the sight towards particular 
objects. Eyelids, also moved by muscles, and fringed by the 
eyelashes, serve to guard the eyes from dust, and screen or shut 
them altogether from the access of too intense a light ; and there 
are glands for the secretion of fluid to moisten the cornea, and by 
the motion of the eyelids keep its surface clear, and in a state 
adapted to yield perfect vision. 

133. As already observed, the eye may be compared to a ca- 
mera obscura, the rays of light from any object entering the pupil, 

What appears to supply the place of the eye in animals which are with- 
out that organ ? 

From what quadrupeds may we obtain specimens, as substitutes, to de- 
monstrate the structure of the human eye ? 

Where is the tunica sclerotica situated ? 

Where the cornea? them's? iheptipil? 

What are the names and positions of the four coats containing the hu- 
mours of the eye ? 

Between which two membranes is the black pigment found ? 

What substance occupies the front cavity of the eye ? 

What is the nature, form, and name of the body which separates this 
from the posterior cavity ? 

With what is the latter cavity filled p 

Draw and describe a magnified section of the eve. 

What is the purpose of the ciliary processes ? 

What name is given to the bony cavity in which the eye is placed ? 

* From the Latin rete a net, in reference to its resemblance to net- 
work. 



376 optics. 

and forming an image on the retina, which produces the percep- 
tion of a visible object conveyed through the optic nerve to the 
brain. That a perceptible image is really formed in this manner 
on the retina, may be experimentally demonstrated by paring away 
the back part of the sclerotic coat of the eye of an ox, with a 
sharp knife, till it becomes so thin as to be transparent: it will 
thus be converted into a miniature camera obscura, and objects 
held before the cornea, will then be seen behind, delineated on 
the retina. 

134. It may be imagined, that if a luminous point, or illumina- 
ted object be placed too near the eye, the rays proceeding from it 
will form an image beyond the retina, or rather the image they 
form on it will be confused and imperfect ; so on the contrary, if 
the luminous point be too distant the image will be confused in 
consequence of the rays converging to a point before they reach 
the retina. 

135. In order therefore that the image may always be formed 
distinctly on the retina, provision must be made for increasing or 
diminishing the refraction of rays within the eye, in proportion to 
the distance of the objects to be viewed. This seems to be effec- 
ted by means of the crystalline humour or lens, which is com- 
posed of concentric laminae of transparent fibres, by the action 
of which its form may be modified so as to adapt the eye to the 
distance of different objects. And in various animals the figure 
of the crystalline, and its situation with regard to the retina are 
varied so as to accommodate the powers of vision in each animal to 
its peculiar circumstances and mode of life. 

136. The vision of objects at different distances may possibly 
also be further facilitated by the variable pressure of the muscles 
on the ball of the eye ; though it must be concluded, from the 
experiments of Dr. T. Young, that their action cannot produce 
any alteration in the shape of the cornea. In viewing near objects, 
the pupil of the eye is contracted, fewer rays enter the eye, and 
such objects are thus distinctly perceived ; while in viewing dis- 
tant objects, the pupil dilates to admit more rays to fail on the 
retina. In obscurity, the pupil of the eye becomes dilated to ad- 
mit as many rays as possible ; and in a strong light its dimensions 
are much contracted, as may be observed by holding a candle 
near the eye of another person. Sudden exposure of the eyes to 
much light produces an uneasy sensation, from the quantity of 
rays admitted through the dilated pupil; and, on passing from 

How can we prove that a perceptible image is formed on the retina at 
the back of the eye ? 

In what cases will images be indistinct? 

What provision is necessary to render objects distinct at different dis- 
tances ? 

By what part of the eye does the adjustment to distances appear to be 
effected ? 

What apparent effect on the exterior appearance is produced by efforts 
to distinguish very distant objects ? 

Whence arises the pain from sudden exposure to a glare of light ? 



ANGLE OF VISION. 377 

open daylight into an obscure apartment, objects are not seen till 
the contracted pupil becomes enough dilated to take in a sufficient 
number of rays to render them visible. 

137. An object may be seen distinctly and singly, though sepa- 
rate images of it be formed on the retina of each eye. This de- 
pends on those images occupying corresponding points on either 
retina, and thus the directions of the optical axes of the two eyes 
intersect each other, and a distinct image is perceived at that 
point. If, however, while a person looks steadfastly at any near 
object with both eyes open, he tries to direct his view to some 
rather more distant object, without suffering the first to escape. at- 
tention, a double image will be perceived, one somewhat above 
the other; and, on ceasing the effort to look beyond the object, 
the images will coalesce into one. Similar effects may be pro- 
duced by pressing with the finger on the ball of one eye, so as to 
displace its optical axis. Double vision is also in the same man- 
ner occasioned by intoxication or by frenzy. Many animals never 
see objects with more than one eye at a time ; as most kinds of 
birds, lizards, and fishes; while there are some species of fish 
that can only see objects situated above them. 

138. Though the perception of visible objects is certainly pro- 
duced by means of their images formed on the retina, yet the 
manner in which the sensation is conveyed by the optic nerves to 
the brain is a mystery which we are utterly unable to penetrate. 
There are also some peculiar relations between the images of ob- 
jects, and the manner in which they are perceived, which have 
given rise to various conjectures, and have never yet been clearly 
explained. Thus, it is certain that the image formed on the retina 
is always inverted with regard to the position of the object pro- 
ducing it ; just like the images formed by a single lens in a ca- 
mera obscura, as may indeed be ascertained by repeating the ex- 
periment on an ox's eye, previously mentioned.* 

139. Some writers on optics content themselves with asserting 
that we really see all objects inverted, but that the judgment cor- 
rects the erroneous perception, a process of the occurrence of 
which no evidence can be produced. Others more philosophi- 
cally attempt to explain this phenomenon by alleging the forma- 
tion of a secondary image within the eye, reflected from that re- 
ceived on the retina to another plane, by means of which the 



When are distinct images formed by both eyes producing a single im- 
pression on the mind ? 

On what does this distinctness depend ? 

How may the two eyes be made to see different images of the same 
object ? 

By what means other than voluntary effort may double vision be pro- 
duced ? 

What peculiarities of sight belong to birds, reptiles, and fishes ? 

In what position is the image of an object formed on the retina ? 

* See No. 133. 
2i2 



37 8 optics. 

position of the image is corrected.* But further investigation is 
requisite to enable us to explain the relation between the visible 
direction of objects, and the position of the images formed by 
them within the eye. 

140. There are, however, some cases in which the judgment, 
with the aid of the other senses, enables us to correct erroneous 
perceptions produced by vision ; and it is thus, by means of the 
sense of feeling and by habitual observation, that we ascertain 
the figures and relative distances of visible objects. It has been 
remarked, that persons born blind from the existence of cataracts f 
in the eyes, on being restored to perfect vision by a surgical ope- 
ration, after arriving at years of discretion, believe at first that 
the objects they see are in immediate contact with their eyes, 
every thing appearing to them as if painted on a plain surface ; 
and they are unable to recognize objects by sight alone, gradually 
acquiring that power by comparing their new sensations with the 
real objects by feeling them. 

141. A person born blind and just restored to sight by the ope- 
ration for the cataract, would not be able to distinguish a die oi 
any other cube from a marble or a billiard-ball, without touching 
them ; neither would he know the persons with whom he was 
most familiarly acquainted, or discriminate his father from his 
mother, or his brother from his sister, without examining their 
persons and dresses by the sense of feeling, or hearing their 
voices. Individuals thus situated acquire the correct sense of 
vision only by degrees, like infants ; and it is by experience that 
they learn to walk about among the objects around, them, without 
the continual apprehension of striking themselves against every 
thing they behold. 

142. The processes by which we judge at all times concerning 
the dimensions and distances of visible objects are, in an analo- 
gous manner, the result of reasoning on visual phenomena ; and 
thus experience modifies considerably the ideas we form of the 
size of any object and its position in space, according to the visual 
angle. For instance, in judging by the visual angle, a man would 
appear to us much smaller at three hundred paces distance than 
at one hundred ; notwithstanding which we are able to form as 
exact a judgment of a man's height at one distance as at the 
other, provided there be other objects at hand which may serve as 
scales of comparison. Thus, we rectify the image formed under 

What means have we of correcting the error of early impressions re- 
ceived through the eye ? 

What happens when persons of mature age are for the first time ena- 
bled to see ? 

How do such persons acquire the correct sense of vision 1 

How do we obtain accurate ideas of the dimensions and distances of 
remote objects ? 

* See a New Theory of Vision. By Andrew Horn. Also Encyclo- 
pedia Metropolitana — Mixed Sciences, p. 459. 
f From the Greek k»t«p«x*ik, a cataract. 



DISTANT VISION. 379 

the visual angle; by our preconceived idea of the common height 
of a man, comparing 1 it in imagination with the door of a house, 
the trunk of a tree, or any other object in view, with the size of 
which we are acquainted. Hence, if we see a man three hun- 
dred paces off, upon a naked plain, as on a wide sandy level by 
the sea-side, he will look very small, and may be mistaken for a 
little child, as we can judge of him only by the visual angle, and 
have no other object near to rectify the erroneous perception. 

143. Dr. Arnott has adduced an interesting example of the op- 
tical effect just illustrated. He says he " once sailed through 
the Canary Islands, and passed in view of the far-famed Peak of 
TenerifFe. It had been in sight during the afternoon of the pre- 
ceding day, at a distance of more than 100 miles, disappointing 
general expectation by appearing then only as an ordinary distant 
hill rising out of the ocean ; but next morning, when the ship had 
arrived within about twenty miles of it, and while another ship 
of the fleet, holding her course six miles nearer to the land, served 
as a measure, it stood displayed as one of the most stupendous 
single objects which, on earth, and at one view, human vision 
can command. The ship in question, whose side, showing its 
tiers of cannon, equalled in extent the fronts of ten large houses 
in a street, and whose masts shot up like lofty steeples, still ap- 
peared but as a speck rising from the sea, when compared with 
the huge prominence beyond it, towering sublimely to heaven, 
and around which the masses of cloud, although as lofty as those 
which sail over the fields of Britain, seemed still to be hanging 
low on its sides. TenerifFe alone, of very high mountains, rises 
directly and steeply out of the bosom of the ocean, to an eleva- 
tion of 13,000 feet, and as an object of contemplation, therefore, 
is more impressive than even the still loftier summits of Chim- 
borazo or the Himalayas, which rise from elevated plains and in 
the midst of surrounding hills."* 

144. Various optical deceptions are produced when we are ob- 
liged to judge of the sizes and distances of objects merely by the 
visual angle. Thus, any person placed at one extremity of a long 
avenue, a gallery, or a rectilineal canal, will perceive the trees of 
the avenue diminishing in height as they are more distant, the 
two ranges of trees seeming to converge towards each other, and 
come to a point if the avenue is very long ; and the two sides of 
a canal, and the floor and lateral walls of a gallery, in the same 
manner, become convergent, and meet in a point when greatly 
extended. These optical effects may be imitated by constructing 

How are we liable to err in estimating the size of a person on a wide 
level surface ? 

In what case may the grandeur of an object be heightened by contrast ? 

What gives the Peak of TenerifFe its peculiar sublimity ? 

Why are the Andes and Himalayas less impressive than that peak ? 

In what cases may the imagination be deceived by an undue reliance on 
the eye ? 

* Elements of Physics, vol. ii. pp. 264, 265. 



380 



c<^ 



a, 

c> - 

'""l-— 3 - 
ef 

^ 

4b 



the sides of a canal or alleys of trees in converging lines, the 
more distant trees gradually diminishing in height; and thus the 
avenue cr canal would appear longer than the reality. 

145. The annexed diagram 
may serve to illustrate the 
apparent diminution of ob- 
jects under different visual 
angles. Suppose a b to be any 
object, as a tree, to an eye si- 
tuated at O, it will appear 
f under the visual angle a O b, 
and the dimensions of the image on the retina will have a certain 
proportion; then, if another tree, c c?, of the same height with 
the first, he placed as far again from it, the visual angle will be 
c O d, and the apparent height of the latter tree will be to that of 
the former, as c' d 1 to a b ; and if a third tree be situated at a fur- 
ther distance, ef, its apparent height will be to that of the first, as 
t' f to a b; that is, the spectator will see three trees really equal 
in height, as if they were three times at the same distance of the 
relative heights, a b, c' d', and e' f. 

146. When objects are extremely distant it is impossible to 
judge correctly concerning their particular situations ; and hence 
an irregular line appears to be an arc of a circle, because we sup- 
pose all the points to be equally distant from us ; and thus when 
stationed in the midst of a plain, remote objects seem to form a 
circle around us. It is for the same reason that the heavens pre- 
sent the appearance of a concave hemisphere sprinkled with stars; 
for at first view the stars seem to be all equidistant from the ob- 
server. A small curved or polygonal line seen afar off appears 
to be a small right line ; a polyedron cut in facets, or an irregular 
mass, at a distance, will look like a sphere, and yet further off 
will exhibit the contour of a flattened disk. This happens with 
respect to the sun and moon, which we see as circular disks. 

147. Optical illusions take place in consequence of the figures 
of bodies in motion. If a sphere revolving on its axis be placed 
at a distance, it will be impossible to perceive the movement, un- 
less there are on its surface spots or visible irregularities, the al- 
ternate appearance and disappearance of which may be observed ; 
and it is thus only that astronomers have been enabled to ascer- 

Ulustrate by diagram the apparent diminution of objects by the effect 
of different visual angles. 

How would a row of trees, of equal heights, and situated equidistant 
from each other, extending nearly in front of the spectator, be made to 
appear by the effect of perspective ? 

How could they be imitated in a picture ? 

In what instances may irregular forms be mistaken for those which are 
regular ? 

What appearance has a spheroidal figure when extremely remote from 
the observer ? 

What will enable us tc judge whether such a body have a rotary mo- 
tion or not ? 



THE THAUMATROPE. 381 

tain the rotation of the sun and the planets, by observing spots on 
their surfaces. 

148. A lighted candle or torch whirled in a circle, the plane of 
which passes through the eye, at a great distance, merely ap- 
pears to come and go, in a line, from one extremity to the other 
of the diameter of the circle. The visible paths of the planets 
through the heavens, in their revolutions round the sun, thus have 
the appparance of right lines, from one extremity to the other of 
which each luminary seems, to a spectator on the earth, alter- 
nately to advance and return. 

149. The impression of light on the eye is not merely instanta- 
neous, but continues during a certain time after the luminous or 
il laminated object has been withdrawn. From the experiments 
of D'Arcy, it has been ascertained that the effect of light on the 
retina remains about 1-7 or 1-8 of a second after the light has ac- 
tually been removed.* To this cause is to be ascribed the circle 
of light formed by whirling round a burning stick, a phenomenon 
with which every one must be acquainted. And on the same 
principle is constructed the amusing toy called the Thaumatrope,} 
contrived by Dr. Paris.:): 




150. It consists of a number of circular cards, having silk 
strings attached to their opposite edges, as represented in the pre- 
ceding figures. By these strings, one of the cards being twirled 
round with a certain velocity, both sides of it will be visible at 
the same time, and any objects traced on them, as a dog on one 
side and a monkey on the other, may be perceived simultaneously. 
Hence the parts of the picture being united, when it is whirled 
round, the monkey will be seen seated on the back of the dog. 
In this case the revolving card becomes virtually transparent, so 
that the objects on opposite sides of it may be viewed together, 

How may a circle be mistaken for a straight line ? 

With what example of this does astronomy furnish us ? 

Does the image of an object vanish from the eye the moment the ob- 
ject is withdrawn ? 

For what length of time has D'Arcy found impressions to remain on 
the visual organ ? 

What familiar and amusing experiments owe their interest to the du- 
rability of visible impressions? 

Describe the thaumatrope. 

* See a Paper " On the Duration of the Sensation of Sight," in Me- 
moires de l'Academie des Sciences, a Paris. 1765? p. 439. 
t From the Greek 0» u/i:4 , a wonder, and Tpsweo, to turn. 
J Philosophy in Sport made Science in Earnest. 



382 optics. 

nearly as they would be if painted on the two surfaces of a plate 
of glass. 

151. An improvement of the thaumatrope, as already described, 
has been made by the inventor, which consists in altering- the 
axis of rotation, while the card is in the act of revolving - , in order 
that the images on its opposite sides may be brought in different 
positions with respect to each other. This is ingeniously effected 
by affixing two strings to one or both sides of the card, which are 
so connected as to act on different points of the border, according 
to the degree of tension applied to them. The appearances ex- 
hibited are thus diversified, and rendered more amusing. A card, 
with a horse on one side and a jockey on the other, may by twirl- 
ing- it be made to show the rider in his saddle, then by merely 
tightening the string, while the card continues revolving, the 
jockey may be seen as if making a summerset over the head of 
his steed : on relaxing the string he will again appear in the sad- 
dle, and by various degress of tension other postures may be dis- 
played. 

152. Many singular effects may be produced by modifications 
of the machinery, all depending on the continuance of the im- 
pression of visible objects on the retina during the space of about 
one-eighth of a second, so that the figures on either side of the 
card, when it is made to revolve, are renewed before the preceding 
impression has ceased its action ; and consequently the figures on 
both sides of the card are seen at the same time. 

153. Another curious machine has been recently invented, 
called the Phantasmascope,* the effect of which further illus- 
trates the phenomenon of the perception of visible impressions 
during a certain period after the objects producing them are with- 
drawn. ' 

154. In this apparatus as modified by Mr. Faraday, figures are 
seen through revolving wheels, or circular disks of pasteboard, 
with deep narrow notches at their edges. If a transparent star, 
highly illuminated, be placed behind a disk of pasteboard or 
blackened tin plate, with a single narrow opening extending from 
the circumference to the centre, it will necessarily hide the whole 
of the star except that part immediately opposite the opening ; 
but if the disk be made to revolve rapidly, the whole star will 
become visible ; as may easily be conceived from what has been 
stated relative to the duration of impressions of light on the re- 
tina. 

By what device has its action been varied ? 

With what, as the least velocity, must this apparatus revolve, in order 
to exhibit its true character ? 

What other toy has been founded on the durability of impressions ? 

What is the arrangement by which figures are viewed in the phantas- 
mascope ? 

How did Faraday contrive to render the whole of an illuminated ob- 
ject visible through a single line of opening ? 

* From the Greek <r>»vr*<rp*, a spectacle, and Sxosm*, to view. 



THE PHANTASMASCOPE. 



383 




155. In the phantasmascope the pasteboard disks are painted 
with a variety of figures, in different positions, and the borders 
of the disks being - cut into cogs or teeth, leaving openings between 
them, when made to revolve on a spindle, on looking at the ob- 
jects as exhibited in a mirror, through the opening, they will dis- 
play the most diversified and grotesque attitudes. 

156. Thus the figures given in the preceding cut, when pro- 
perly viewed, would all appear to be pirouetting like so many 
opera-dancers. By different arrangements of the openings, and 
varied designs, may be exhibited, in a similar manner, yawning 
figures, jumping frogs, creeping serpents, and a multiplicity of 
other strange combinations. 

157. One of the most curious facts relating to the faculty of 
vision is the absolute insensibility to the impression of light at a 
certain point of the retina, so that the image of any object falling 
on that point would be invisible. When we look with the right 
eye this point will be about 15 deg. to the right of the object ob- 
served, or to the right of the axis of the eye, or the point of most 

For what purpose is the mirror introduced in the exhibition of the 
phantasmascope r 

Are all the parts of the retina equally sensible to the impressions of 
lisht ? 



381 optics. 

distinct vision. When looking with the left eye the point will he 
as far to the left. The point in question is the basis of the optic 
nerve; and its insensibility to light was first observed by the 
French philosopher Mariotte. 

1 58. This remarkable phenomenon may be experimentally proved 
by placing, on a sheet of writing paper, at the distance of three 
inches apart, two coloured wafers, then on looking at the left-hand 
wafer with the right eye at the distance of about a foot, keeping 
the eye straight above the wafer, and both eyes parallel with the 
line which joins the wafers, the left eye being closed, the right- 
hand wafer will become invisible ; and a similar effect will take 
place if we close the right eye, and look with the left. Accord- 
ing to Daniel Bernoulli, this insensible spot is about 1-7 part of 
the diameter of the eye. 

Chromatics, or the Theory of Colours. 

159. Among the properties of light one of the most striking and 
curious is that of communicating colours to bodies. Popular lan- 
guage ascribes the existence of colours to some inherent qualities 
of the substance on whose surfaces we perceive them ; and thus, 
in using the phrases a red brick or a green wafer, an uninformed 
person would conceive the redness of the brick, or the green tint 
of the wafer, to be as much peculiar properties of those bodies as 
the quadrangular shape of the one and the circular figure of the 
other. But we find, from experiment, that though colour partly 
depends on the texture of substances, and the nature of their sur- 
faces, the essential efficient cause of colour is light, since not 
only are bodies destitute of colour in the absence of light, but, as 
will be subsequently shown, their colours may be altered by sub- 
jecting to certain modifications the light by which they are ren- 
dered visible. Hence it happens, that many coloured objects, the 
peculiar tints of which are discriminated without difficulty in 
broad day-light, appear to wear the same hue in the dusk of the 
evening, or by candle-light. It may therefore be properly stated, 
that the colour of a substance is the effect of light on a surface adapted 
to reflect its peculiar colour. 

160. The influence of light, in the production of colour is re- 
markably modified by refraction. This effect of light is most con- 
veniently exhibited by means of a triangular prism of glass. If 
such a prism be held with one of its angular edges opposite to 

What fact, in regard to this subject, was discovered by Mariotte ? 
How is the existence of a point of insensibility experimentally proved ? 
What is the size of the insensible spot ? 

What is the usual belief and the common language of mankind in re- 
gard to the existence of colours? 

What is the efficient cause of colours ? 

How is this proved ? 

What is the true definition of colour ? 

What relation has colour to refraction ? 

How is the influence of refraction best exhibited ? 



CAUSE OF COLOURS. 



385 



the eye, the objects seen through it will not be doubled, as when 
viewed directly through one of the flat sides of the glass, bat 
they will be more or less elongated, according to the angle at 
which the prism is held, and will also be clothed with all the co- 
lours of the rainbow. 




White 



161. The dissection of a ray of solar light into different colours, 
6y refraction, may be more accurately displayed by admitting a 
ray through an aperture in a window-shutter into a darkened cham- 
ber, and causing it to fall on a diaphanous prism A B C, as re- 
presented in the preceding figure. A ray D thus entering, and 
suffered to pass unobstructed, would form on a plane surface a 
circular disk of white light E, but the prism being so placed that 
the ray may enter and quit H at equal angles, it will be refracted 
in such a manner, as to form on a screen M N, properly placed, 
an oblong image called fhe solar spectrum, and divided horizon- 
tally into seven coloured spaces, or bands of unequal extent, suc- 
ceeding each other in t)<>i order represented : red, orange, yellow, 
green, blue, indigo, violet. 

162. These bands are s iot separated by distinct lines, so that it is 
difficult to determine whyre one ends and another commences, the 
several tints at their borders being blended, and each almost im- 
perceptibly united with those next it ; the whole spectrum exhibit- 
ing the seven principal colours, with intermediate shades or mix- 
tures. Indeed some writers enumerate but six colours in the spec- 
trum, omitting the indigo ; and Dr. Wollaston observed, that when 
a very small ray was submitted to the prism, there were only four 
colours, namely, red, yellowish-green, blue, and violet. Bands of 



Describe the effect of a prism of any transparent substance when placed 
near the eye. 

How is the separation of white light into its constituent coloured rays 
most advantageously displayed ? 

What is the image of a beam of light refracted by a prism usually de- 
nominated ? 

Into how many and what spaces is the solar spectrum divided ? 

What are the two extremes of the spectrum ? 

What fact in regard to. the number of colours was observed by l)r 
Wollaston ? 

2 K 



386 optics. 

colours more precisely terminated may, however, be obtained by 
receiving the ray on a lens before it is allowed to fall on the prism ; 
and the image thus formed will be more extended in length and 
very narrow. 

163. Similar phenomena may be produced by means of other 
kinds of light as well as that of the sun ; and all transparent, sub- 
stances, in masses not terminated by parallel surfaces, have in 
some degree the same effect as the glass prism. Hence the dia- 
mond, sapphire, topaz, and other precious stones cut in facets, 
display the prismatic colours ; as also do angular crystals of quartz, 
Iceland spar, and many saline and stony substances ; the cut-glass 
ornaments of lustres, &c, exhibit the same glittering tints, by 
lamp-light ; and the refraction of the sun's rays in passing through 
drops of water produces a like effect in the rainbow. 

164. From the preceding and many other experiments of a simi- 
lar nature, Sir Isaac Newton was led to the construction of a 
theory relating to the cause of light and colours, which was, during 
a long period, almost universally received among men of science. 
The production of coloured spectra by the refraction or reflection 
of light had been observed long before Xewton commenced his 
researches, and some imperfect attempts had been made to explain 
the phenomena; but he not only showed that these conjectures 
were wholly unsatisfactory, but also proposed a highly ingenious 
hypothesis, founded on the doctrine of the emanation of light, or 
that system which refers the phenomena of vision, light, and 
colours, to the presence and motion of an ethereal fluid, constantly 
issuing from the sun and other luminous bodies. " The sun's 
direct light," says Professor Maclaurin, "is not uniform in respect 
of colour, not being disposed in every part of it Jo excite the idea 
of whiteness which the whole raises ; but, on the contrary, is a 
composition of different kinds of rays, one sort of which, if alone, 
would give the sense of red, another of orange, a third of yellow, 
a fourth of green, a fifth of light blue, a sixth of indigo, and a 
seventh of violet ; that all these rays together, by the mixture of 
their sensations, impress upon the organ of sight the sense of 
whiteness, though each ray always imprints there its own colour ; 
and all the difference between the colours of bodies when viewed 
in open daylight arises from this, that coloured bodies do not re- 
flect all sorts of rays falling upon them in equal plenty ; the body 
appearing of that colour of which the light coming from it is most 
composed."* 

165. Hence, according to the theory of emanation, white light 

By what means may distinctness between the coloured bands be ob- 
tained ? 

Is the presence of solar light necessary to the production of colours bj 
refraction ? 

How did Newton explain the phenomena of the spectrum ? 

How did the Newtonian philosophers conceive light to be constituted ? 

Of what did they suppose white light to be composed ? 

* Maclaurin's Philosophy of Newton, 4to. b. iii. p. 518. 



CHROMATIC REFRACTION. 387 

is an assemblage of molecules of various colours, which may be 
separated from each other by the action of a prism; and bodies, 
when exposed to the rays of the sun, display any given colour 
because they are so constituted as to absorb all the molecules ex- 
cept those of the rays of their own peculiar colour : thus perfectly 
white substances absorb none of the molecules, but reflect the 
white or compound light unaltered; black substances absorb all 
the rays, and therefore yield no colour; and red, yellow, and blue 
substances respectively reflect those rays alone by which they are 
distinguished. 

166. The least that can be said in favour of this system is that 
it accounts for all the phenomena ; but it must be admitted that 
the notion of material particles perpetually traversing space in all 
directions, with almost infinite velocity, is absolutely gratuitous, 
and hardly consistent with the simplicity and economy generally 
observable in the works of nature. The appearances likewise 
may be explained by having recourse to a different theory, advan- 
ced by Huygens, and advocated by Euler, which refers them to 
the excitement and propagation of undulations through an ethe- 
real fluid pervading all space, which, by inconceivably rapid vi- 
brations conveys white or coloured light to the eye, in a manner 
analogous to that in which musical and other sounds are brought 
by slower vibrations of the air to the ear. 

167. "Every simple colour," according to this system, "de- 
pends on a certain number of vibrations which are performed in a 
certain time ; so that this number of vibrations made in a second, 
determines the red colour, another the yellow, another the green, 
another the blue, and another the violet, which are the simple co- 
lours represented to us in the rainbow. If, then, the particles of 
the surface of certain bodies are disposed in such a manner, that 
being agitated, they make in a second as many vibrations as are 
necessary to produce, for example, the red colour, I call such a 
body red : and rays which make such a number of vibrations in 
a second may, with equal propriety, be denominated red rays ; and, 
finally, when the optic nerve is affected by these same rays, and 
receives from them a number of impulsions, sensibly equal, in a 
second, we receive the sensation of the red colour. 

168. The parallel between sound and light is so perfect that it 
holds even in the minutest circumstances. When I produced the 
phenomenon of a musical chord, which may be excited into vibra- 
tion, by the resonance only of certain sounds, you will please to 

"What account did they give of bodies possessing a white colour ? what 
of those which are black ? 

To what objections is the Newtonian theory of emanations liable ? 

What more simple view of the subject was entertained by Huygens, 
Euler, and others ? 

On what, according to that theory, do the several colours depend } 

In what manner does this theory conceive coloured bodies to be adapted 
to produce the sensations belonging to their several tints? 

What analogy has been traced between the seven colours and the seven 
notes of the musical gamut ? 



388 optics. 

recollect, that the one which gives the unison of the chord in 
question is the most proper to shake it, and that other sounds af- 
fect it only in proportion as they are in consonance with it.*. And 
it is exactly the s?me as to light and colours ; for the differen 
colours [of the solar spectrum] correspond to the different musical 
sounds. "7 

169. It ought to be observed that while the phenomena of light 
and colours may be accounted for according to the system of ema- 
nation or that of undulation, it is not absolutely necessary to adopt 
either in reasoning concerning them ; and it will be sufficient here 
to state that rays of light, whether they be trains of material par- 
ticles, issuing from luminous bodies, or chains of undulations 
taking place in an ethereal medium, are always propagated in 
right lines till they enter or impinge on a refracting or reflecting 
medium,- when they are either bent at certain angles, or returned 
in the same lines in which they advanced ; and thus, when a 
luminous ray is refracted or reflected it still proceeds in a right 
line, though that line may not be parallel with its original direc- 
tion. 

170. If the coloured image obtained by means of a glass prism be 
extended longitudinal!}", by making it first pass through a convex 
lens, it will be found that the rays of different colours possess dif- 
ferent degrees of refrangibility, or are some relatively more refracted 
than others. The red tint which forms the inferior band of the 
spectrum produced by the apparatus above described, consists of 
rays which have undergone a smaller degree of refraction than those 
which constitute the orange tint, the latter are somewhat more re- 
fracted than the yellow rays, the refraction is greater in the other 
rays successively, and most considerable in the violet ra3 r s, which 
therefore form the colour of the superior band of the spectrum. 

171. If after the solar spectrum has been rendered more distinct, 
by subjecting a beam of light to a lens before it is refracted by 
the prism, an aperture be made in the screen, on which it is re- 
ceived, opposite to any one of the coloured bands, a small pencil of 
light similar to that of the band will pass through, and if it be 
refracted bjr a second prism, and even again by a third, and then 
received on another screen, it will not be decomposed any further, 
but will produce a circular image of a uniform , colour correspond- 
ing with that of the band of which it originally formed a portion. 

172. By a similar method the various refrangibility of the dif- 

In what circumstances in regard to direction do rays of light resemble 
currents of sound ? 

What directions do rays always pursue after refraction ? 

How are the differently coloured rays" found to be constituted in respect 
to refrangibility? 

Which colour is the least refrangible } which the most? 

What effect is produced on any one of the coloured bands of the spec- 
trum, by an attempt to decompose it by a second refraclion ? 

* See Treatise on Acoustics, No. 58, 59. 

+ Euler's Letters to a German Princess. Ed. 1823. vol. i. p. 85. 



CHROMATIC DIFFRACTION. 389 

ferently coloured rays may be further demonstrated. For this 
purpose it is only necessary to make the first prism revolve slowly 
on its axis, and thus each part of the spectrum will transmit its 
rays successively through the aperture in the first screen, and 
form a succession of little circular images on the second, traced 
at different heights, the violet colour appearing strongest, the red 
weakest, and the intermediate tints varying as they are nearer to 
one or the other. Thus may be produced an ascending or descend- 
ing procession of images on the screen, by turning the first prism 
in one direction or the other. 

173. Rays of light, when reflected, exhibit properties analo- 
gous with those which they show when refracted ; those coloured 
rays which are most refrangible being also the most refiexible ; so 
that the violet is reflected more readily than the indigo, the latter 
more than the blue, and the others in succession becoming less 
and less refiexible, and the red least of all. This order of reflex- 
ibility explains in some measure the azure tint of the heavens ; 
for the atmosphere being a reflecting medium, those rays most 
subject to reflection, namely, those which are violet, indigo, 
and blue, are reflected most abundantly, and hence the appearance 
of the unclouded celestial vault. To a similar cause is to be attri- 
buted the bluish tints of distant mountains, often imitated with great 
effect by landscape painters, in the display of aerial perspective. 

174. As the decomposition of solar light into variously coloured 
rays may be exhibited by the means already stated, so there are 
methods by which white light may be composed by uniting- 
the different colours of the solar spectrum into one image. This 
may be most perfectly effected by causing the spectrum to pass 
through a convex lens, and receiving the image on a card or screen 
placed in the focus of the lens, where a circular disk of white 
light will be formed. A mixture of seven powders tinted as the 
prismatic colours, and in the proportions of the breadths of the 
several corresponding bands will produce a whitish compound ; 
and seven coloured wafers fixed at proper distances on the border 
of a circular apiece of pasteboard would, when it was whirled 
round, on a pin passing through its centre, display a wheel or 
circle of a hue more or less approaching to white. 

175. Instead of reuniting all the rays of the prismatic spectrum 
by means of a lens, certain parts may be united, a screen being 
placed to intercept the others, when the image produced will not 
consist of white light, but of particular tints resembling some 
of the simple colours of the spectrum. Thus the yellow and the 
blue will form a green, the yellow and red an orange, or the red 

How may the degree of refrangibility belonging to each colour be veri- 
fied by a second retraction ? 

What order do the colours follow in the degree of their reflexibility ? 

How is this principle applied to explain atmospheric and other colours ? 

How may a beam of white light be formed out of the constituent ele- 
ments of different colours ? 

How may the compound colours be formed from the parts of the spec- 
trum ? 

2 k 2 




390 optica 

and blue a violet tint; but these artificial colours are distinguisha- 
ble from the original colours corresponding with them by their 
susceptibility of decomposition into their constituent parts when 
transmitted anew through a prism. However, though certain 
colours thus reunited form coloured mixtures, there are other 
colours which when united by a second transmission through a 
convex lens reproduce white light ; and these are termed comple- 
mentary colours. 

176. As the coloured rays that compose white light have diffe- 
rent degrees of refrangibility, it follows that a pencil of rays of 
light, as E F, in the marginal figure, 
falling on a lens AB, the violet rays 
being the most refrangible will be 
brought to a focus sooner than the 
other rays, as at C, and the red rays 
which are the least refrangible wil. 
meet in a focus as at D, the inter 
mediate rays meeting at relative dis- 
tances between those two points. Hence the images which are 
formed at the focus of a lens will be surrounded b} r various colours 
constituting what is termed an iris. It is likewise obvious that 
those rays which enter the lens near its border will be more dis- 
persed than those which pass through near its axis. Thus when 
an object is viewed through a single glass lens, the parts of it 
most distant from the centre will be deformed, and as just ob- 
served surrounded by a coloured irradiation. 

1/7. It has been shown that rays of light in passing through 
different transparent mediums are more or less refracted or di- 
verted from their original direction ; and that the degree of refrac- 
tion which light undergoes varies with the medium through which 
it passes. The manner also in which light is affected by being 
made to traverse a refracting substance the sides of which are not 
parallel to each other, as a prism of glass or crystal, has been 
stated ; and the phenomenon of the production of coloured light, 
from the dispersion or analysis of the rays of white light has been 
generally illustrated. 

178. Sir Isaac Newton, in making his original experiments on 
solar light with a glass prism, ascertained that the relative 
breadths of the coloured spaces in the prismatic spectrum, sup- 
posing its whole extent to be divided into 360 parts, would be 
for the red stripe, 45 parts ; Tor the orange, 27 ; for the yellow, 48 

Give some examples of this mode of producing intermediate colour 

What are meant by complementary colours ? 

What effect has the difference of refrangibility in the rays of light i> 
on the colour of an image formed behind a lens ? 

With what do such images appear to be surrounded ? 

What circumstance causes variations in the degree of refraction suf- 
fered by light ? 

What facts did Newton discover in re^ x to the relative breadth of 
solar bands in the spectrum ? 



DISPERSIVE POWERS OF. DIFFERENT BODIES. 



391 



for the green, 60; for the blue, 60; for the indigo, 40; and for the 
violet, SO. These numbers, however, are by no means constant, 
depending- on the peculiar nature of the refracting body employed 
to dissect a ray of white light; and it is a very singular circum- 
stance, that though Newton made use of prisms composed of dif- 
ferent substances in the prosecution of his researches, yet he ne- 
glected to observe that the dispersion or divergence of the diffe- 
rently coloured.j-ays is greater when produced by one refracting 
medium than by another: he therefore erroneously concluded that 
the refractive and dispersive powers of bodies always correspond- 
ed; but that is far from being the case. 

179. The effects of a considerable number of transparent solids 
and fluids on rays of solar light transmitted through them have 
been ascertained by Sir D. Brewster and other scientific inquirers, 
and tables of their dispersive powers have been constructed, from 
which it appears that the dispersive and the refractive powers of 
various bodies hold no definite proportion to each other. 

180. The effect of prisms composed of different refracting sub- 
stances on a ray of white light may be explained by reference to 
the following figures. Oil of cassia and sulphuric acid are trans- 
parent liquids which exhibit great diversity of dispersive power. 
Suppose A B to represent a spectrum, such as would be formed 
by transmitting a solar Tay through a prism having its sides of 

glass, and filled with oil of cassia; and 
A! B', a similar spectrum produced by a 
prism iilled with sulphuric acid. Then 
it will appear that the least refrangible 
colours, red, orange, yellow, numbered 
1, 2, 3, will be more contracted in the 
spectrum A B, or that formed by the oil 
of cassia, than in A/ B', or the spectrum 
formed by sulphuric acid ; and that the 
most refrangible colours, blue, indigo, 
violet, 5, 6, 7, will be more expanded 
in the former spectrum than in the lat- 
ter : the centre of one spectrum lying 
just within the blue space in the line 
C C, and in the other that line dividing 
the green space, but less unequally. 
Hence the coloured spaces bear not the 
same proportion to each other as the lengths of the spectra ; and 

Do the numbers obtained by him appear to be constant for all refract- 
ing bodies ? 

Into what error was he led in respect to the dispersive power of re- 
fracting media ? 

What general statement is true in regard to the refractive and the dis- 
persive powers of different substances ? 

Construct and explain the diagram illustrating the difference between 
the dispersive power of a prism of sulphuric acid and one of oil of cassia. 

In which colour is the centre of the spectrum formed by the acid .' 

In which colour is the centre of that formed by the oil ? 




392 optics. 

this want of correspondence is termed the irrationality of disper- 
sion, or irrationality of the coloured spaces in the spectrum. 

181. On this inequality of dispersive power among transparent 
bodies depends the construction of those optical instruments called 
achromatic,* or aplanatic,f telescopes; by means of which the 
coloured fringes and other defects in images formed by a single 
lens are removed, or prevented from interfering with the distinct 
observation of the object. The principle on which this is affected 
is by combining together refracting substances possessing diffe- 
rent dispersive powers, in such a manner that the aberration caused 
by one shall be counteracted or neutralized by the opposite effect 
of the other. 

182. Suppose a compound prism A B C, as represented in the 
diagram below, to be formed by joining two prisms A C D, and 
DCB, composed of the same substance; then if a ray of white 
light be made to fall on it, an image of the spectrum will be ob- 
tained, the colours of which will be less distinct than they would 

have been if the prism A C D alone had been 
employed, because the light decomposed by 
the first prism will be partially recom- 
posed in passing through the second ; and 
it would be entirely so, if B C were pa- 
rallel to A B ; because then the second 
prism having the same dispersive power 
as the first, would be so placed as to coun- 
teract its effect. If, instead of employing 
*-' two prisms of the same kind, one of the 
prisms D B C, be composed of a substance the dispersive power 
of which is much stronger than that of the other, ADC, the rays 
dispersed in passing through the former prism will be re-collected 
by the second, and an achromatic prism will thus be formed. If 
the refringent power, likewise, of the prism D B C be the same 
with that of the prism ADC, the refraction will not be corrected ; 
but if the refringent power of D B C is the greatest the refrac- 
tion will be in some degree corrected. 

183. It is practically impossible to form a perfectly achromatic 
prism, because the dispersive power of different transparent sub- 
stances differs with respect to the differently coloured rays. But 

What is meant by the irrationality of dispersion? 

What advantage is derived from the knowledge of dispersive powers 
in the construction of optical instruments ? 

Explain the terms achromatic and aplanatic. 

How may the dispersive power of a prism be counteracted ? 

Does it necessarily follow that the refractive effect must be overcome 
by a second refractor which restores the white colour of a previously re- 
fracted beam ? 

Why can we not form perfectly achromatic prisms ? 

* From the Greek *, privative, and Xp«if*«, colour : without colour, 
f From », privative, and nx*vn, error or deception : without error. 




ACHROMATIC LENSES. 393 

the effect may be produced with regard to any two colours ; and 
it is therefore usual to take the extremes of the spectrum, namely 
the red'and violet, or the red and blue. 

184. If, as Sir Isaac Newton too hastily concluded, the disper- 
sive property and the refringent power had in all substances in- 
creased and diminished in the same ratio, the refraction, as well 
as the dispersion produced by one substance would be counter- 
acted by another : the rays emerging after the double refraction 
would thus become parallel. It would hence have been impossi- 
ble to achromatize a lens ; for if a compound lens were formed by 
uniting a convex with a concave glass in such a manner that the 
rays should become deprived of colour after issuing from it, they 
would resume their original parallel direction : that is the colori- 
zation and the refraction produced by the convex glass would be 
destroyed both together by the concave one, and the rays could 
•not, therefore, be united in a focus. 

185. The effect of single convex lenses in producing an indis- 
tinct image with a coloured fringe, termed chromatic aberration, 
previously noticed, will be such that, "for parallel rays, the circle 
of least chromatic aberration, or of least colour, will have the 
same absolute magnitude, whatever be the focal length of the lens, 
provided the aperture remains the same. Now since in a tele- 
scope (with a given eye-glass) the image is magnified in propor- 
tion to the focal length of the object-glass, it follows, that by in- 
creasing the focal length the magnitude of the image increases, 
while that of the coloured border remains the same : by con- 
tinuing, therefore, to increase the focal length we get an image so 
much magnified that the colour bears an insensible proportion to 
it. Hence, as long as simple lenses only were used, in order to 
correct the aberrations and secure a due quantity of light, it was 
necessary to have telescopes of very unmanageable length. Some 
of those constructed by Huyghens were of one hundred and even 
one hundred and fifty feet focal length."* 

186. Newton, after numerous attempts to render refracting tele- 
scopes more portable and effective, found himself foiled, in conse- 
quence of the incorrect opinion he had formed concerning the 
correspondence of the dispersive with the refringent powers of 
bodies, and therefore inferring that "the improvement of the re- 
fracting telescope was desperate,""]" he devoted his future attention 

What would have been the success of such an attempt had Newton's 
supposition been true ? 

What is the effect of a single convex lens in producing an image ? 

In what proportion to the focal length of the object-glass will be (he 
magnifying power of a telescope ? 

What inconvenience arose from the use of simple lenses in the con- 
struction of refracting telescopes? 

* Short Elementary Treatise on Experimental and Mathematical Op- 
tics. By the Rev. Ba'den Powell, M. A., F. R. S. Oxford, 1S.33. p. 101 
f Optics. Lond. 1701, 4to. Part T. Prop. vii. Theor. 6. 



394 optics. 

to the construction of telescopes of a different kind, in which the 
images of objects are formed by reflection.* 

187. But that which was despaired of by this great man has 
fortunately been accomplished by others. The merit of having 
first discovered the method of forming an achromatic refracting 
telescope appears to be due to Mr. Chester More Hall, a gentle- 
man residing in Essex, England, who, about 1733, had completed 
several achromatic object-glasses, by the combination of lenses 
of different kinds of glass, having different degrees of dispersive 
power. In 1747, Leonard Euler published a paper in the Me 
moirs of the Academy of Sciences at Berlin, on the improvement 
of refracting telescopes. This attracted the attention of seve 
ral philosophers to the subject, among whom was John Dollond, 
an eminent optician in London, who having fully ascertained the 
diversitjr of dispersive power in different substances, found that 
an achromatic lens might be formed by joining together crown 
glass, or that kind with which windows are glazed, with flint 
glass, or that of which cut-glass vessels and ornaments are made. 

188. Peter Dollond, the son of the optician just mentioned, 
made a further improvement by forming an object-glass of three 
instead of two lenses, including a concave lens of flint glass be- 
tween two convex lenses of crown glass. It is now, however, 
most usual to emplo)' only two lenses, one, partly concave, of flint 
glass ; and the other, double convex, of crown glass. These 
glasses have different curvatures, and are formed in sach a man- 
ner that, after refraction, the red rays and the violet rays will be- 
come reunited at the same point : the intermediate rays will also 
be reunited at nearly the same point, it being impossible to reunite 
all the rays in precisely one point (as above stated), though they 
may be made to approach it sufficiently to prevent the usual effect 
of chromatic aberration. 

189. In the marginal figure, represent- 
" -k ing' the section of a compound lens, the 

ray E F falling on the centre of the lens 
A B, will pass through it without any al- 
teration; but another ray G H falling on 
one side of the centre will be divided, and 
the violet ray, as being the most refrangi- 






\m: 



ST- 



Z^-"\, ble, will pass through the convex lens in 



" the line H I, but the red ray in the line 
H K. The concave lens of flint glass 
will make both these rays diverge from the 
axis E F, the red taking the direction K L, 
and the violet the direction I N ; and in 
passing again through the air to the focus, 
the red ray will take the direction L F, and 

Who first succeeded in overcoming this difficulty ? What two mate- 
rials did Dollond employ for the formation of achromatic lenses ? 

* See subsequent part of this Treatise, relative to Optical Instruments 



CAUSE OF THE RAINBOW. 395 

the violet the direction N F : both consequently will be reunited 
at the point F. 

190. Achromatic lenses thus constructed are still subject to im- 
perfection, and hence subsequent attempts have been made to im- 
prove them, which have been attended with a considerable degreo 
of success. Dr. Robert Blair, of Edinburgh, between 1787 and 
1790, having conceived the idea of employing transparent fluids 
in the construction of compound lenses, at length succeeded, by 
inclosing muriatic acid, properly prepared, between glass lenses, 
in forming an object-glass by which the differently coloured rays 
were all bent from their rectilineal course with the same equality 
and regularity as by reflection. Other experimental philosophers 
have occupied themselves in analogous researches ; and especially 
Mr. Barlow, of Woolwich, who has been very successful.* To 
the instruments thus constructed it has been proposed to apply the 
term apla?iaiic, or free from error, as possessing the utmost degree 
of accuracy. 

191. Among the most interesting natural phenomena is that of 
the rainbow, the production of which wholly depends on the re- 
fraction and reflection of the sun's rays by clouds or drops of rain, 
and the consequent formation of prismatic colours ; and the sub- 
ject may therefore here be properly noticed. The bow in the 
heavens, as the French correctly term it (Farc-en-ciel), is seen 
when the sun darts his rays on a cloud dissolving in rain, and the ob- 
server places himself opposite to it, with his back turned to the sun. 
Sometimes one bow only is perceived, but more usually there are 
two bows, the interior or lower one exhibiting brighter colours 
than the other, the tints of which are comparatively pale. Both 
present the colours of the prismatic spectrum ; but in the interior 
bow the tints gradually ascend from the violet to the red, while in 
the exterior bow the violet is most elevated. Some writers remark 
that a third bow has been observed, but very rarely ; and accor- 
ding to theory many bows must be formed, though all beyond the 
second must, in general, be utterly imperceptible. 

192. The colours of the rainbow are the result of the decom- 
position of white light, in its passage through the globular drops 
of water forming a shower of rain. Each coloured ray produced 

In what manner is it customary, at present, to arrange the parts of an 
achromatic lens ? 

Of what material is the double convex lens composed ? 

Which two rays are brought together at the focus of an achromatic 
lens ? 

Trace in the diagram the respective courses of the red and the violet 
rays. 

What method was adopted by Blair and Barlow to form their aplanatic 
instruments ? 

On what principle is the rainbow formed ? 

In what order are the colours arranged in the double rainbow ? 

Whence do the colours of the celestial bow proceed ? 

* See Philosophical Transactions for 1S28; or Abstract of Papers iu 
Philos. Trans., vol. ii. pp. 333, 334. 



396 optics. 

by this decomposition traverses the globule, and is reflected in 
part at the opposite concave surface ; it then traverses the globule 
again in a new direction, and presents itself to escape towards 
the observer. A part only, however, actually passes out, and the 
other part is again reflected and carried back into the interior of 
the globule. In this manner a multitude of successive reflections 
may be caused, at each of which some portion of the light will 
escape, but its intensity becomes more and more feeble with the 
increase of the number of reflections. 

193. It is from those rays that thus first issue from the drop on 
the side towards which the observer is looking that the effect is 
produced. The rays which pass out from a globule after having 
suffered one or more reflections form a certain angle with their 
primitive direction. This angle is constant for all rays of the 
same nature that penetrate the globule at the same incidence, and 
which undergo within it the same number of reflections; but it 
varies for those rays the incidences of which are different, and 
which undergo a greater or smaller number of reflections. 

194. It will appear from calculation that in a series of parallel 
rays of the same nature, which fall on a globule, and which un- 
dergo but one reflection within it, that the angle will be succes- 
sively augmented, from the normal or direct ray, at which there 
will be no angle, to a certain limit, beyond which it will decrease 
till the ray becomes a tangent to the sphere or globule. Hence 
within those limits, the parallel rays entering the globule very 
near together, and undergoing deviation not very dissimilar, will 
remain sensibl}' - parallel at their escape : and therefore an eye 
placed in the direction of such a bundle of ra)'s will be affected 
with a sufficiently vivid sensation of colours ; while elsewhere 
encountering only isolated rays, the sensation produced will be 
extremely inconsiderable. The rays which thus issue from a glo- 
bule so as to form a small bundle capable of making a sensible 
impression, are termed efficacious rays. 

195. It is the same with regard to rays which undergo two re- 
flections, or a greater number, within the globule. There will 
always be certain limits within which several parallel rays, near 
together, issuing from the globule and remaining sensibly parallel, 
will produce a distinct sensation on the eye. These limits are 
not the same for all kinds of coloured rays, but vary with their 
refrangibility. Thus, with respect to the red rays, which are the 
least refrangible, when the ray issues after one reflection, it makes 
with the incident ray an angle of 42° 2'; this angle is succes- 

How many reflections occur before the light leaves a drop of water to 
pass to the eye of the observer in constituting the primary rainbow ? 

What general fact can be stated in regard to the angle formed by rays 
passing out of a drop of water after undergoing one or more reflections? 

What is meant by the normal ray in a beam of light ? 

Which of the rays reflected from rain-drops are termed efficacious ? 

What causes the difference in the position of the several sets of effica- 
cious rays ? 

Whatangle with the incident ray, does the efficacious red ray make ? 



IRIDISCENT CIRCLES. 397 

srfely smaller for the other coloured rays, to the violet, which is 
the most refrangible, and for which it is 40° 17'. When the emer- 
gent ray undergoes two reflections in the interior of the globule, 
the limit in the case of the red rays will be at an angle of 50° 57', 
and in the case of the violet rays, at an angle of 54° 7'. 

196. The formation of the coloured bands of the rainbow may 
be thus explained : the sun, considered as a simple luminous point 
at an infinite distance, transmits to the shower a bundle of rays, 
of which each globule of water receives some. Hence on each 
of the globules fall some efficacious rays, which pass off to ob- 
servers at different points. Thus, the first coloured ray which 
can come to an observer, after a single reflection in the globule, 
will be that which makes the smallest angle v/ith its original direc- 
tion ; and will therefore be the violet ray, of which the angle 
is 40° 17'. 

197. All the globules situated in the same circle, to the centre 
of which the axis of the bundle is incident, will produce the same 
sensation, and consequently form the first coloured line. The effi- 
cacious red rays which form with their original direction an angle 
of 42° 2', will produce the last or highest line of the first bow ; 
and between these extremes there will be the five other colours of 
the prismatic spectrum, in the order of their refrangibility. Such 
is the mode of formation of the first or principal bow : its dimen- 
sions will be the difference between 40° 17' and 42° 2', and there- 
ore equal to 1° 45'. 

198. Beyond the red rays the observer will only perceive those 
which have undergone two reflections, and their intensity will con- 
sequently be more feeble. The first rays in this case will now 
be the red, which make the smallest angle, equal to 50° 57' ; 
forming the commencement of a secondary bow, at a distance from 
the first, corresponding with the difference between 42° 2' and 
50° 57', and therefore equal to 8° 55'. The last or highest line 
of the second bow will be the violet, of which the rays will make 
with their original direction, an angle of 54° 7', and between these 
extremes will be found the other colours. The dimensions of the 
second bow will be 54° 7'— 50° 57 / =3° If/. 

199. It may readily be understood from the preceding observa- 
tions how three or more bows may be formed by successive re- 

What angle is made by the efficacious violet with the incident ray, after 
a single reflection ? 

What are the angles respectively for these two rays after undergoing 
two reflections ? 

How is the formation of coloured bands in the rainbow explained ? 

What is the necessary limit to the breadth of the interior or primary 
bow ? 

What rays will come to the eye of the spectator beyond the red ray of 
that bow ? 

What order of colours will be observed in the exterior bow ? 

What is the breadth of band between the two bows ? 

What is the breadth in degrees of the secondary bow ? 
2 L 



398 optics. 

flections ; and why also they must be too faint to be perceptible.* 
We have supposed the sun reduced to a luminous spot, and thus 
a circular line only of each colour would be produced ; but as the 
sun has a sensible diameter, it follows that each band of the bows 
must have certain dimensions depending on the apparent diame- 
ter of the sun. 

200. Lunar rainbows occasionally occur, but in most cases they 
are faint or colourless, from the inferior intensity of the moon's 
reflected light. Coloured halos are also sometimes seen, but they 
are among the more unusual meteorological phenomena. Clouds 
of rare colours, as green, have been noticed by some observers ;f 
and the effect may be traced to the same causes with the more 
frequent and beautiful rainbow. 

Why are not lunar bows generally distinguishable ? 
What other phenomenon analogous to the rainbow is occasionally ob- 
served in the atmosphere ? 

* Under peculiar circumstances, more than two rainbows, or rather 
iridiscent circles, may be formed by the refraction of the sun's rays, so 
as to be distinctly visible. A remarkable instance of such a phenomenon 
is related by Professor Winkler, from "L'Histoire General des Voy- 
ages," as occurring to the French and Spanish philosophers who were 
employed, in the last century, in measuring a degree of the meridian, in 
Peru. "As Don Antonio de Ulloa was with the French Academicians 
on the high and desert mountain of Pambamarca, id the kingdom of 
Quito, each of them saw his own image over against the side on which 
the sun rose, as in a mirror, and the head of each image encompassed 
with three rainbows, having all one and the same centre. The last or 
outmost colours of the one rainbow touched the first of the following. 
And externally, round all the three circles, but at some distance from 
them, a fourth bow appeared, which showed white only. When one of 
the spectators moved from one side to the other, the whole appearance 
followed him, in the like form and order. And though the observers 
were six in number, and stood quite close together, yet each could see 
only his own image, and not those of the others. As the figures of their 
bodies were portrayed in the middle space of the encompassing rainbow, 
the vapours of this space must have been in the state for the incident and 
reflected rays to form equal angles." — Elem. of JYat. Pldlos. JDelin., vol. 
ii. pp. 63, 64. 

t The following instance of the occurrence of this phenomenon is de- 
rived from a diary kept by the person who witnessed it : December 24, 
1812. Just before sunset, I observed a line of clouds, situated above the 
sun, tinged of a most beautiful pea-green colour. Above and below the 
green clouds were situated clouds of a dusky purple hue, intermixed with 
narrow stripes of orange. As the sun was sinking below the horizon the 
green belt of clouds became gradually lighter ; and when the orb of day 
ceased to be seen, the green tinge also vanished. This appearance con- 
tinued about a quarter of an hour." 

Musschenbroek notices the occurrence of green clouds, and observes 
that " such were seen by Frezier, and are described in his ' Voyage to the 
West Indies.' "—Eletn. of J\"at. Philos., translated from the Latin, by 
Colson. 1744. vol. ii. p. 241. 



COLOURS OF THIN PLATES. 399 



Colours of thin Plates, 

201. The phenomena of coloured rings observed in the simple 
experiment of blowing bubbles of soap and water ; in thin films 
of oil of turpentine or other essential oils floating on water; on 
the surface of polished steel when heated ; and in general in thin y 
plates of transparent substances, as quartz, Iceland spar, and mica, 
are extremely curious, as exhibiting a peculiar mode of the de- 
composition of white light. It may be most conveniently studied 
by examining what takes place when a very thin stratum of air 
or any other fluid is confined between two plates of glass ; and 
the experiment may be advantageously made by placing a convex 
lens of small curvature upon a concave lens of a radius somewhat 
greater, and on pressing them together the colours will appear 
arranged in the form of rings round a central spot, which if the 
pressure be sufficiently powerful will be perfectly black, when 
viewed by reflected light, but when examined by transmitted 
light, as by looking at the sky through the glasses, instead of pla- 
cing the eye between the light and the reflecting surface, the cen- 
tral spot will be white, and be surrounded by rings, the colours of 
which will be complementary to those seen by reflection. Henc6 

it appears that the colours seen by reflection and by transmission 
of white light through thin plates, are those which form the great- 
est contrasts with each other. 

202. The coloured rings are seen in the following order, pro- 
ceeding from the centre to the circumference, forming different 
series of tints. 

Colours of thin plates viewed by reflection. 
1st series. Black, blue, white, yellow, orange, red. 
2d series. Violet, blue, green, yellow, red. 
3d series. Purple, blue, green, yellow, red. 
4th series. Bluish-green, red. 

Colours of thin plates viewed through the glasses. 
1st series. White, Yellowish-red, black, violet, blue. 
2d series. White, yellow, red, violet, blue. 
3d series. Green, yellow, red, bluish-green. 
4th series. Red, bluish-green. 

Under what different circumstances are transparent bodies capable of 
exhibiting coloured rings ? 

How is the appearance most conveniently studied ? 

In what different positions must the eye be placed with reference to the 
glasses to observe the two different classes of phenomena ? 

Of what colour is the central point in two conjoined lenses when it is 
viewed by transmitted light.'' 

What difference do reflected and transmitted light respectively produce 
on every ring of the coloured surface ? 

What is the order in each of the four series of colours when viewed by 
reflected light ? 

What is it when viewed by transmitted light? 



400 optics. 

203. These tints are none of them identical with the simple 
prismatic colours. Sir J. Herschel observes, respecting the re- 
flected colours, that " the green of the third order (or series) is 
the only one which is a pure full colour, that of the second being 
hardly perceptible, and of the fourth comparatively dull, and ver- 
ging to apple-green ; the yellow of the second and third orders 
are both good colours, but that of the second is especially rich 
and splendid ; that of the first being a fiery tint passing into 
orange. The blue of the first order is so faint as to be scarce sen- 
sible, that of the second is rich and full, but that of the third 
much inferior : the red of the first order hardly deserves the name, 
it is a dull brick colour ; that of the second is rich and full, as is 
also that of the third; but they all verge to crimson, nor does 
any pure scarlet or prismatic red occur in the whole series."* 

204. The breadths of the rings are unequal, becoming narrower 
and more crowded, as they recede from the centre ; and the extent 
of the rings or circles depends on the curvatures of the glasses 
between which they are formed. In order to make experiments 
with accuracy a proper apparatus is requisite. That used by Sir 
Isaac Newton, in experiments on this subject, consisted of a 
plano-convex lens, the radius of the convex surface of which was 
twenty-eight feet, and a double convex lens, the radius of whose 
surfaces was fifty feet ; and the latter being placed on the convex 
surface of the former, they were held together, with any required 
degree of pressure, by three pairs of screws, fixed at equal inter- 
vals on their borders. 

205. The colours may be shown by reflected light, by pressing 
together with the fingers a concave and a convex glass slightly dif- 
fering in curvature, that of the former having the largest radius ; 
but it is impossible by this means to maintain equable pressure, 
and the figures become distorted from circles into irregular ovals, 
or angular lines. Hence it will be obvious that no correct obser- 
vations can be made on the dimensions of the coloured rings, unless 
the glasses can be subjected to uniform pressure. It is also ne- 
cessary that the eye of the observer should always be similarly pla- 
ced, or at the same angle of obliquity; for if the obliquity bechanged, 

[low do the colours correspond with those of the prismatic spectrum ? 

Which of the reflected colours is perfect in its kind ? 

What relations have the breadths of the several rings to their distance 
from the common centre ? 

On what do their actual breadths depend ? 

What were the forms and curvatures of the lenses used by Newton in 
experiments on coloured rings ? 

In what simple manner may the rings be exhibited by reflected light ? 

How must the apparatus be arranged and secured, in order to a cor- 
rect appreciation of the nature of the rings ? 

What precaution is necessary in regard to the eve of the spectator ? 
Why ? 



Encyclopxd. Metropol. — Mixed Sciences, vol. ii. p. 463. 



COLOURED RINGS. 401 

by elevating 1 or depressing - the eye or the glasses, the diameters 
(but not the colours) of the rings will change. 

206. It is of importance to the explanation of this phenomenon 
to ascertain the thicknesses at which the respective tints, or the 
several points of greatest brightness and greatest obscurity occur. 
This may be done by means of Newton's apparatus ; for the co- 
loured rings being- perfectly regular, by exactly measuring their 
diameter, may be found the thickness of the plate of air corre- 
sponding to each of them ; for the interval between a plane and 
a spherical surface, the centres of which are brought into contact, 
will increase in the ratio of the squares of the distances from 
that point of contact. 

207. Hence Newton found that in the most brilliant parts of 
the circles the thicknesses followed the progression 1, 3, 5, 7, 9; 
while in the darkest parts, commencing with the centre, they 
followed the progression 0, 2, 4, 6, 8. The same philosopher 
ascertained that when water is substituted for air between the 
glasses, the proportions of the diameters of the rings will be the 
same, but they will be relatively smaller; whence it follows that 
the plates of water reflecting any given colours must be more at- 
tenuated than those of air. It further appears that glass plates, 
to reflect the same colours, must be thinner than those of water ; 
and it may be generally concluded that the thinness of the plates 
increases in proportion to the density of the bodies of which they 
are composed, or rather in proportion, to their refracting powers. 

208. Air in a plate but half a millionth of an inch in thickness 
ceases to reflect light ; and the same is the case with water at 
three-eighths of the millionth of an inch, and with glass at one-third 
of the millionth of an inch. A plate of air two millionths of an inch 
in thickness, exhibits what Sir I. Newton terms " the beginning 
of black." A plate nine-millionfhs of an inch reflects the red of 
the first circle or series ; one nineteen-millionths of an inch the 
red or scarlet of the second series ; and tables have been calcu- 
lated of the thicknesses of plates of air, water, and glass respec- 
tively, for each colour of each of the four series given above, and 
also for those of three more series, which may be observed ex- 
tending in narrower circles beyond the preceding. Air seventy- 
How may we ascertain the thickness of those plates of air which pro- 
duce the different rings ? 

In what ratio do the distances between a plane and a sphere to which it 
touches, increase from the tangent point ? 

What did Newton ascertain to be the relative thicknesses of the strata 
at the brightest parts of the rings ? 

What progression of numbers represents the thicknesses of the darkest 
rings P 

What law did Newton find to prevail when the space between his len- 
ses was filled with -water instead of air? 

What result was given by glass ? 

What general conclusion was derived from a trial of various sub- 
stances ? 

How much must the plates of each substance be diminished before they 
lose the power of reflecting light ? 

2 r, 2 



402 optics. 

seven-millionths of an inch in thickness reflects a reddish-white 
colour, forming the boundary of the seventh or outer circle ; and 
beyond that thickness it reflects quite white or undecomposed light. 

209. As to the cause of the coloured rings formed by thin plates, 
Newton proposed an explanation founded on the doctrine of the 
emanation of light as consisting of molecules traversing space ; 
and his hypothesis is deserving of notice as being in some degree 
applicable to the undulatory theory, which represents light as 
arising from the vibrations of an ethereal medium. 

210. Having ascertained from experiment that the different rays 
become reflected at the successive thicknesses 1, 3, 5, 7, &c, and 
transmitted on the contrary, at the intermediate thicknesses-0, 2, 4, 
6, &c, he regarded these laws as resulting from a particular dis- 
position of the luminous molecules, which he denominated " fits 
of easy reflection," and " fits of easy transmission." Thus he 
concluded that any ray would be thrown into a fit of easy reflec- 
tion on falling on a plate the thickness of which was one of the terms 
of the series 1, 3, 5, 7, 9, &c. ; 1 being the first or least thickness 
at which it became susceptible of being reflected ; and on the 
other hand, a ray would be in a fit of easy transmission when the 
thickness of the plate was one of the terms of the series 2, 4, 6, 
8, &c. 

211. Thus far Newton's hypothesis is little more than an enun- 
ciation of facts, but he also conjectured that the fits of easy re 
flection and transmission might depend on a sort of magnetic po 
larity belonging to the particles of light ; to which supposition , 
however, it does not appear that the illustrious author himself 
attached any great importance. 

212. According to the undulatory theory both of the surfaces 
of the thin lamina are concerned in the production of the colours ; 
and the interference of the light reflected from the second surface 
with the light reflected from the first interrupts or facilitates the 
passage of the ray at certain intervals of thickness of the plate.* 

213. "The colours of natural bodies in general are the colours 
of thin plates, produced by the same cause which produces them 
in thin laminae of air, glass, &c. ; viz., the interval between the 
anterior and posterior surfaces of the atoms, which, when an odd 
multiple of half the length of a fit of easy reflection and trans- 
mission for any coloured ray moving within the medium, obstructs 
its penetration of the second surface, and when an even, ensures 
it. The thickness, therefore, of the atoms of a medium, and of 

What was Newton's explanation of the cause of coloured rings ? 

Explain by an example what he meant to express by "Jits of easy reflec- 
tion and of easy transmission." 

On what what were the^s supposed to depend ? 

How is the undulatory theory applied to explain the coloured rings ? 

What is supposed to determine the colour reflected by surfaces receiv- 
ing light with a perpendicular incidence ? 

* See Powell's Elem. Treatise on Optics, pp. 138—146 



DOUBLE REFRACTION OF LIGHT. 40H 

the interstices between them, determines the colour they shall re- 
flect and transmit at a perpendicular incidence. Thus, if the 
molecules and interstices be less in size than the interval at which 
total transmission takes place, or less than that which corresponds 
to the edge of the central black spot in the reflected rings, a me- 
dium made up of such atoms and interstices will be perfectly 
transparent. If greater, it will reflect the colour corresponding 
to its thickness."* 

214. There are several very curious optical phenomena arising 
from the interference of the rays of light, besides the colours ex- 
hibited by thin plates; and among these may be included the va- 
riable colours of fine fibres and striated surfaces. " Fine fibres 
and striee give beautiful colours by interference, when single, be- 
tween ra3^s reflected from their opposite sides; and when many 
are placed together, more complex colours are produced by their 
combined interferences. 

215. " A striking example of this kind is seen in the iris buttons, 
invented by Mr. Barton, the surface of which is covered with 
minutely-engraved parallel lines, in some instances not more than 
one 10,000th of an inch apart. A phenomenon very similar is 
that of the colours exhibited by the surface of mother-of-pearl. 
This substance, when examined by a powerful microscope, is 
found to present a surface covered with minute striaj arranged in 
parallel waving lines. "f 

Double Refraction of Light. 

21 G. Repeated instances have been already adduced of the ap- 
pearance of double or multiplied images of bodies viewed through 
transparent media ;X Dut these phenomena are all conformable to 
the common law of optics, which indicates the correspondence 
between the angles of incidence and of refraction or reflection, 
and the relation of their sines to each other. 

217. There are, how r ever, many cases in which a different effect 
is produced by the transmission of light through certain transpa- 
rent substances, as some kind of salts and crystalline spars, plates 

When would a medium be found perfectly transparent? 

What other phenomena hesides that of coloured rings depend on the 
interference of rays of light ? 

To what purpose in the arts has the colorific effect of grooved surfaces 
been applied ? 

What natural suhstance exhibits the effect of iridescence in consequence 
of possessing a striated surface ? 

In how many different ways may multiplied images be produced ? 

What is the peculiar effect of those substances which are denominated 
double refracting ? 

* Encyclopsed. Metropol. — Mixed Sciences, vol. ii. p. 580. 

f Powell's Elem. Treatise on Optics, p. 150. See also Paper&.in the 
Philosophical Transactions, 1814 and 1829, by Sir I). Brewster; and Abstr. 
of Papers in Philos. Trans., vol. i. pp, 502—504; and vol. ii. pp. 378,379. 

X See 108, this treatise. 



404 optics. 

of which having- parallel surfaces, when any object is viewed 
through them exhibit a double image, instead of a single one like 
similar plates of glass. Such bodies are called doubly refracting 
substances, and the property they possess, double refraction 
A B C D 



218. This mode of refraction may be experimentally demon- 
strated by means of a small plate of Iceland spar, or crystallized 
carbonate of lime, not more than £ of an inch in thickness. If a 
plate of glass be placed over either or all the preceding figures, A, 
B, C, D, each will appear singly, as to the naked eye; but if a 
plate of Iceland spar be held above one of the figures, a double 
image will be perceived, as two dots, two circles, or two lines in- 
stead of one. 

219. The distance between the two images will depend on 
the thickness of the plate of spar. If it be £ of an inch thick, 
the images will be so near together that the little circle B will 
look like a figure of 8. There is, however, another circumstance 
which will influence the relative separation of the images ; and 
that is the position of the plate ; for if it be laid flat on the paper 
and slowly turned round horizontally, one of the images will be 
perceived to revolve round the other ; so that the circle will in 
one position appear thus 8, and in another thus oo ; and the lines will 
coalesce and diverge successively, as the plate is made to revolve. 

220. In explanation of this phenomenon it may be stated that 
a ray of light on entering into the transparent spar becomes di- 
vided into two portions, one of which follows the ordinary law of 
refraction, as to the ratio of the sine of the angle of incidence to 
that of the angle of refraction, while the other undergoes a sepa- 
rate refraction, according to a new and extraordinary law. The 
Iceland spar consists of rhomboidal crystals, masses of which 
are always reducible by natural cleavage into exact rhomboids, 
having each of their faces equal and similar rhombs. These 
are the forms of the molecules into which the mass can be sepa- 
rated by continued subdivision ; and in every one of these rhom- 
boids the short diagonal is called the optical axis. 

221. Thus in the annexed figure the diago- 
nal line C represents the axis of the rhomboi- 
dal solid A B. Now if a ray of light is trans- 
mitted through a crystal in the line of its op- 
tical axis no double image will be formed, and 
the ray will be refracted simply according to 
the ordinary law of the proportional sines ; for 
in this case the ordinary and extraordinary rays, 

By what substance may this property be exemplified ? 
What kind of images are seen through plates of Iceland spar? 
What circumstance determines the amount of separation ? 
On what do the relative positions of the two images depend ? 




BOUELY REFRACTING CRYSTALS. 



405 



as they have been termed, will coincide. But in all other cases 
the law is essentially different, the ray becoming divided, and 
one part of the pencil will be refracted, according to a law of a 
very singular and complicated nature. 

222. A plane passing through the axis is called a principal sec- 
tion ; and if a ray be incident, so that the ordinary refraction takes 
place in the plane of a principal section, then for all the inci- 
dences, the ordinary ray having its index of refraction constant, 
the extraordinary ray will also be in the same plane, though with 
an index of refraction which varies according to its position. If 
the ordinary refraction be in a plane perpendicular to the axis, the 
extraordinary ray will also in this case be in the same plane, and 
the index of refraction of the ordinary ray remaining of course 
constant, that of the extraordinary ray will also be constant.* 

223. Hence it appears that both the ordinary and extraordinary 
rays have a certain relation to the optical axis of the crystal ; "all 
the phenomena being the same, as though some power emanat- 
ing from that axis had produced that extraordinary refraction, by 
separating a portion of the light from the original ray in its trans- 
mission through the prism, and attracting it towards the axis, or 
repelling it from it. Sometimes the extraordinary refraction is nega- 
tive, or a deflection further from the axis, as in the Iceland spar; 
and sometimes it is positive, or a deflection nearer to the axis, as 
in common quartz crystal; but it is always with the axis that the 
angle of extraordinary refraction is made."f 

224. A considerable number of crystalline substances are found 
to possess analogous properties, though with some modifications, 
depending on their peculiar structure. Thus some crystals have 
only one axis of double refraction, while others have two or more 
such axes. Dr. Brewster ascertained that all those hodies which 
crystallize in the form of the rhomboid, the regular hexaedral prism, 
the octaedron with a square base, and the right prism with a 
square base, have but one axis of double refraction; some, like 
the Iceland spar, having negative axes, as tourmaline, alum-stone 
sapphire, emerald, and phosphate of lime ; while a smaller num- 
ber, as quartz, zircon, and oxide of tin, have positive axes. 

226. Among the crystals which have two axes of double re- 
How is the phenomenon in question explained ? 

What is the form of crystal in the Iceland spar ? 

What is meant by the optical axis of such a crystal ? 

What is meant hy its principal section ? 

How will the two refractions take place where the ordinary refraction 
is made the plane of a principal section ? 

How when it is made in a plane perpendicular to the axis ? 

When is the extraordinary refraction negative, and when positive P 

How do crystals of different substances vary from each other in their 
doubly refracting power ? 

What forms of crystal have but one axis of double refraction ? 



* Powell's Elementary Treatise on Optics, p. 121. 
f Readings in Science, p. 148. 



406 optics. 

fraction, are glauberite and sulphate of iron. But with respect 
to these bodies, as also the crystals with many planes of double 
refraction, and those with circular double refraction, the effects 
follow a very complicated law ; and M. Fresnel made the remark- 
able discovery that in such cases neither of the images is refracted 
according to the ordinary law, but that both undergo a deviation 
from their original plane, exhibiting- a sort of complicated double 
refraction.* 

226. The property of double refraction was first discovered in 
the Iceland spar, by Erasmus Bartholin, a Danish philosopher, 
towards the close of the seventeenth century ; it was particularly 
investigated by the celebrated Huygens ; and the subject has in 
our own times acquired a peculiar interest in consequence of its 
intimate connexion with polarization. 

227. Concerning the nature of Polarization of Light, Ave can 
only afford room for Sir David Brewster's concise account of the 
discovery of this propert3 T of light, which was made by M. Malus, 
colonel of the imperial corps of engineers, who, in 1810, published 
a most valuable memoir on double refraction, for which he gained 
the prize offered to the writer of the best work on that topic, by 
the Institute of France. 

228. M. Malus, " having accidentally turned a doubly refract- 
ing prism to the windows of the Palace of the Luxembourg, which 
were at the time illuminated by the setting sun, he was surprised 
to observe that one of the double images of the windows vanished al- 
ternately during the rotation of the prism ; and after various fruitless 
speculations on the cause of this singular phenomenon, he was 
conducted to the great discovery, that light reflected at a particular 
angle from transparent bodies, is polarized like one of the rays pro- 
duced by double refraction. 

229. " This singular result opened a wide field of inquiry to phi- 
losophers : and the successive labours of Malus, Arago, Biot, 
Fresnel, and Cauchy, in France; Seebeck and Mitscherlich, in 
Germany; and Young, Herschel, and Airy, in England — present 
a train of research ' than which,' as a distinguished philosopher 
remarks, ' nothing prouder has adorned the annals of physical 
science since the developement of the true system of the uni 
verse.'"f 

What crystals have more than one axis of this kind ? 
What did Fresnel discover in regard to the two images formed by crys- 
tals with ninny planes of double refraction ? 
By whom was double refraction discovered ? 
From what is its greatest importance derived ? 
What investigation led Malus to the discovery of polarization? 
What incident first opened the way to this discovery ? 
What is the general result at which he finally arrived ? 

* See Sir J. Herschel's Discourse on (he Study of Natural Philosophy, 
pp. 30—33. 

f Report on the recent Progress of Optics ; by Sir D. Brewster, in Re- 
port of the British Association for 1832, p. 314. For further information 



INVENTION OF SPECTACLES. 407 



OPTICAL INSTRUMENTS. 

230. There are two principal kinds of optical instruments ; 
namely, those which may be more properly styled dioptrical, as 
they consist of one or more lenses, their effects depending- on the 
refraction of light; and those called catadioptrical instruments, in 
the construction of which lenses and mirrors are combined, and 
hence telescopes of this description have been termed reflecting 
telescopes, to distinguish them from other telescopes, whose pow- 
ers depend on refraction alone. 

231. The perfection of these instruments must consist in the 
excellence of the lenses and mirrors of which they are formed, and 
of the accuracy of their arrangement, so that the axes of the re- 
spective glasses may be situated in a right line. They must be 
placed one behind the other, at distances exactly calculated with 
reference to their several foci. The eye must also be placed at a 
fixed point for observation. That lens in a telescope or microscope 
which is nearest the observer is named the eye-glass; and the 
lens or mirror which is turned towards the object to be examined 
is named the object-glass. The eye-glass is usually fixed in a 
tube, and so arranged that its distance from the object-glass may 
be varied according to circumstances. 

Spectacles. 

232. The employment of convex or common spectacles, or a* 
least of single convex glasses to assist the sight, must have been 
coeval with the knowledge of the magnifying power of convex 
lenses. The invention of spectacles has been ascribed by some 
to Alessandro Spina, an Italian, who died in 1313 ; * and accord- 
ing to others the inventor was a Florentine nobleman, named Ar- 
mato Salvini, who died in 1317. f It may not improbably be in- 
ferred, from these statements, that the mode of adapting two con- 
vex lenses to a frame, so as to form a pair of spectacles, originated 
about the close of the thirteenth century. But the magnifying 

Into how many classes are optical instruments divided ? 
On what principles of construction is this distinction founded ? 
On what does their excellence depend ? 

n what positions must the several glasses of a telescope be placed in 
respect to each other ? 

What names are given to the several glasses ? 
At how early a period were spectacles invented ? 

relative to Double Refraction and Polarization of Light, the reader is re- 
ferred to the Treatise on those subjects published by the Society for the 
Diffusion of Useful Knowledge ; and to the very valuable Essay on Light, 
by Sir John Herschel, in the Encyclopaedia Metropolitana, of which a 
French translation, enriched with Notes, by MM. Yerhulst and Quetelet, 
has been printed at Paris. 

* V. Redi Epistola ad Falconerium. 

t V»Acta Lipsiensia, Ann. 1740. 



408 orncs. 

properties of convex lenses or some similar transparent bodies was 
certainly known at an earlier period, though we are ignorant of 
the precise manner in which they were used. 

233. There is a very remarkable passage in a treatise of Roger 
Bacon on "The Secret Works of Art and Nature," in which he 
says, " Transparent bodies may be so figured that one thing may 
be made to appear many, and one man an army ; and several suns 
and moons may be rendered visible at pleasure. * * * * 
* * Thus also things which are afar off may be brought near, 
and on the contrar}*" ; so that from an incredible distance we might 
read very small letters, and distinguish the numbers of things col- 
lected together, though extremety minute ; and make the stars ap- 
pear when we please.* Thus it is thought that Julius Cassar, 
from the sea-coast of Gaul, observed by means of very large glasses 
(specula), the disposition and site of the camps and towns of 
Britannia Major."f 

234. This celebrated writer also thus expresses himself relative 
to the refraction of light, in his " Opus Majus :" " Greater things 
than these may be performed by refracted vision. For it is easy 
to understand, by the canons before-mentioned, that the greatest 
things may appear exceedingly small, and contrarily. For Ave 
can give such figures to transparent bodies, and disperse them 'n 
such order, with respect to the eye and the objects, that the rays 
shall be refracted and bent towards any place we please, so that 
we shall see the object near at hand, or at a distance, under any 
angle we please; and thus from an incredible distance, we may 
read the smallest letter, and may number the smallest particles of 
dust and sand, by reason of the greatness of the angle under which 
we may see them : and on the other hand, we may not be able to 
see the greatest bodies close to us, by reason of the smallness of 
the angle under which they may appear. For distance does no£ 
affect this kind of vision, except by accident, but the quantity of 
the angle does. And thus a boy may appear to be a giant, and a 
man as big as a mountain ; because we may see a man under as 
large an angle as the mountain, and as near as we please. And 
thus a small arm) 7- may appear to be a very great one, and though 
very far off, yet seem very near us; and contraril3 T . Thus like- 
wise the sun, moon, and stars may be made to descend hither in 
appearance, and be visible above the heads of our enemies; and 
many things of a similar nature may be effected which would as- 
tonish unskilful persons." 

235. From the manner in which Bacon, in the preceding pas- 
sages, notices the effects of refracting substances in modifying the 

What evidence is derived from ancient authors, proving that lenses 
were known before the invention of spectacles ? 

* This must apparently be understood of a telescope, or some such in- 
strument, by means of which the stars may be seen in broad daylight. 

t Epist. Fr, K. Bacon, de Secretis Operibus Artis et Naturse, et de 
]S T ullitate Magise. Hamburg. 1572. Cap. 5. De Ejcpcvientiis Per.pectivis 
Artificialibus. 



EFFECT OF CONVEX SPECTACLES. 409 

power of vision, it can hardly be doubted that single lenses, at 
least, were sometimes used for other purposes than those of mere 
experiment; though the general employment of spectacles to as- 
sist the visual organs of aged persons or others, may be dated 
from the beginning of the fourteenth century, or just after the pe- 
riod when they are said to have been invented at Florence. 

236. There are two distinct kinds of spectacles, namely, those 
with convex glasses, which magnify objects, or bring their images 
nearer to the eyes ; and those with concave glasses, which diminish 
the apparent size of objects, or extend the limits of distinct vision. 

237. In old persons the transparent cornea becomes more flat- 
tened than in youth, and probably the crystalline humour under- 
goes a corresponding alteration, in consequence of which the rays 
coming from objects do not converge to a focus, so as to form a 
distinct image on the retina, unless they are relatively at a con- 
siderable distance from the eye. Hence it happens, as may be 
often observed, that aged persons when they attempt to read or 
examine a minute object, without spectacles, are usually obliged 
to hold the book, letter, or other object at arm's length. Such 
long-sighted individuals are termed presbytes* The manner in 
which they may be assisted by convex glasses may be illustrated 
by the annexed diagram. 




238. Let C D be supposed to represent a section of the crystal- 
line lens, and A B a similar section of a spectacle lens, then the 
object O, at about six inches from the eye, will form a perfect 
image on the retina, at R; but if the latter lens be removed, the 
object at the same distance will become confused, and in order to 
obtain a proper view it must be withdrawn to treble or perhaps 
four times that distance, and if it be very small, the unassisted eye 
may not be able to distinguish it at any distance. 

239. Those called short-sighted persons are such as have the 
transparent cornea unusually prominent, and therefore the rays 

How are we to suppose that single lenses had been used before the time 
of Bacon ? 

How many kinds of spectacles are employed ? 

What is the effect on the size and apparent distance of obiects of those 
vhich have convex glasses ? 
What is the effect of concave spectacles ? 
What parts of the eye undergo changes from age ? 
To what expedient do persons thus affected have recourse in reading r" 
What form of spectacle lenses do these changes render necessary ? 
Explain the figure illustrating the effect of such lenses. 

* From the Greek npg<r5«j, an old man. 

2 M 



410 OPTICS. 

from objects entering their eyes converge to a focus before they 
reach the retina, unless any object be placed very near the eye.* 
Where this peculiarity of vision exists but in a slight degree, 
it is rather an advantage than otherwise, as the individuals are 
thus gifted with a kind of microscopic sight; for they can see 
smaller objects than are commonly discerned by others, and are 
merely obliged to hold them relatively nearer to the eye. Distant 
objects, however, can only be seen confusedly ; and hence the ad- 
vantage such persons derive from concave spectacles. The na- 
ture of the assistance which these glasses afford will appear from 
considering the following diagram. 




240. Let C D, as before, represent a section of the crystalline 
lens, then the rays from the object O will be rendered somewhat 
divergent in their passage through the concave glass A B, so that 
the effect of the prominent cornea on them will be diminished, and 
they will form a perfect image on the retina at R; whereas if the 
concave glass were removed, the rays would come to a focus 
before they reached the retina, and diverging again the image 
would be confused. 

241. Common convex spectacles and reading-glasses, especi- 
ally if they magnify considerably, have the defect of deforming 
more or less objects not viewed through the centre of the lens. 
For the rays which issue from distant objects and reach the eye 
through the borders of a lens, falling on it obliquely, are more re- 
fracted than the other rays, and hence the images become confus- 
ed. To remedy this inconvenience Dr. Wollaston proposed em- 
ploying concavo-convex lenses, with the concave sides turned 
towards the eyes; "and spectacles thus constructed, called peri- 
scopicf spectacles, if accurately made, and adapted to the peculiar 
degree of long-sightedness which they are intended to relieve, 
will be found far superior to those constructed as usual with 
double convex lenses. 

What is the cause of short-sightedness ? 
What advantage is possessed by short-sighted persons ? 
What inconveniences do they suffer ? 

Where is the image formed in the eye of a short-sighted person ? 
Draw and explain the diagram illustrating the effect of concave spec- 
tacles. 

What defect have convex spectacles of high magnifying power ? 
How did Dr. Wollaston propose to remedy this defect ? 

* Short-sighted persons are called in Latin Myopes, from the Greek 
Mv u, to wink or half-shut the eyelids, and v.h, the eye. 

f From the Greek n«pi, about, around, and Sjcoj^ to look. 



INVENTION OF THE MICROSCOPE. 411 

242. The Esquimaux, inhabiting- a country covered with snow, 
would be subject to a weakness of vision approaching- to blindness 
but for the method they take to guard their eyes from the constant 
stimulus of the bright white light reflected from the objects around 
them. For this purpose they use a sort of spectacles which they 
call snow-eyes, formed of small pieces of wood or bone, with a nar- 
row slit in the middle, which are fixed near the eyes, by strings 
or thong-s passing round the head, so that no light can reach the 
eyes, except that which enters through these apertures. These 
rude instruments not only protect the wearers from the excess of 
light, but also enable them to distinguish more readily distant 
objects.* 

243. Persons whose sight is so much impaired that they find spec- 
tacles nearly useless may derive great benefit by viewing objects 
through conical tubes without glasses, but having only a small 
aperture at the end furthest from the eye, and blackened in the 
inside. Such tubes may be fitted into a frame and worn like spec- 
tacles ; and they may be rendered more serviceable by being so con- 
structed as to be lengthened or shortened, and have the apertures en- 
larged or diminished at pleasure. 

The Microscope, j- 

244. The transition from the use of a single lens to assist 
vision to that of combinations of lenses for viewing small objects 
may be conceived to be by no means difficult; yet it appears that 
three centuries elapsed between the invention of spectacles and 
that of the microscope. Huygens attributes the invention of the 
latter instrument to Cornelius Drebbel,^: about 1621; others to 
the famous Galileo, or to F. Fontana, a Neopolitan ; and it is 
extremely probable that the idea may have occurred to different 
persons engaged in scientific pursuits, about the same period. 

245. The simple microscope is merely a single convex lens of 
high magnifying power ; and it may consist of a globule of glass, 
formed by holding a small fragment of flint glass on a piece of 
iron wire, flattened at the end, in the flame of a spirit-lamp, and 
letting it drop, when fused, on a sheet of paper placed to receive 
it. The globule must then be fitted into an aperture drilled in a 
small plate of brass ; or if the glass fragment be placed in the 
first instance over such an aperture in a thin plate of platina, it 

What expedient do the Esquimaux adopt to screen their eyes from the 
excessive light reflected from the snow ? 

What expedient may be adopted when the eyes are too much weakened 
to be aided by spectacles ? 

How long- did the invention of spectacles precede that of microscopes ? 

To whom has the invention of the microscope been attributed ? 

What is the construction of the single microscope ? 

How may lenses for such a microscope be constructed ? 

* V. Sigaud de la Fond Elem. de Phys., t. iv. p. 192. 

t From the Greek Mixpsjj minute, and ZxoVsm. 

| See Treatise on Pvronomics, No. 51. Huygens Dioptrics, p. 221. 






412 



OPTICS. 



may be fused by exposing it to the flame, and becoming fixed in 
the little hole, it will form a microscope ready mounted. Such 
microscopes must necessarily have very short foci, and can there-, 
fore be used only for examining extremely minute objects. The 
magnifying power of lenses are inversely as their focal lengths : 
thus a convex lens whose focal distance is 2 inches, will increase 
the linear dimensions of the image of an object 5 times ; and a 
lens the focal distance of which is 1-10 of an inch will magnify 
an object 100 times as to linear extent, and 10,000 times as to su- 
perficial extent. -«. 

246. The compound microscope 
must consist of two or more con- 
vex lenses. The object-glass is a 
small lens of very short focus ; and 
there may be one or several eye- 
glasses. Among the most usual 
forms is the microscope with three 
glasses : but various modifications 
have been adopted, with a view to. 
the improvement of these instru- 
ments, by forming' both the eye- 
pieces and the objectives of two or 
more glasses. 

247. The effect of the compound 
microscope may be described by 
means of the accompanying dia- 
gram, which represents the object A 
B placed a little beyond the object- 
glass C D ; then the rays issuing 
from it would form an image at A' B', 
while the lens E F diminishes the 
convergence of these rays, whence 

it follows that the image is formed at A" B". This latter image 
becomes the immediate object of vision, seen by the eye through 
the lens G H, and therefore at A"' B'", greatly magnified. 

The Telescope.* 

1. REFRACTING TELESCOPES. 

248. The invention of the telescope is usually stated to have 
taken place about 1590 ; but it is manifest from the writings of 

To what purpose is the use of a microscope thus constructed necessa- 
rily limited ? 

Of how many lenses must the compound microscope be composed t 

Which is the more common form of this instrument ? 

Draw and explain a diagram representing the essential parts of the 
compound microscope. 

What is the purpose of the second lens ? 

In what position is the image seen with reference to that of the object r 

How early did the invention of the telescope occur ? 

* From the Greek tv.-, afar, and x'xos-i*. 




THE REFRACTING TELESCOPE. 413 

Roger Bacon, already referred to, as well as from other sources 
of intelligence, that the effect of combinations of optical glasses 
must have been ascertained by experiment, long before that period, 
though the arrangement of them so as to form telescopes, and 
their general application to the purposes of science may be dated 
from the time just mentioned. Accident is supposed to have led 
to the discovery of this important instrument, which has been va- 
riously attributed to Zachary Jansen, or to John Lippersheim, who 
were Dutch spectacle-makers ; and the improvements made on 
these perspective as they were styled, by Galileo, John Baptist 
Porta, Simon Marius, and others, may account for their being some- 
times represented as the inventors of the telescope. 

249. The most simple kind of refracting or dioptrical telescope 
is that termed the astronomical telescope, consisting of two con- 
vex lenses, an object-glass and an eye-glass, the foci of which 
concur in the same point 




Let A B represent rays from some distant object, as a star, then 
the image formed by the object-glass C D, being viewed through 
the eye-glass G H, will have its apparent diameter magnified ac- 
cordingly. Thus, if the object-glass have a magnifying power 
equal to 10, and that of the eye-glass be equal to 6, the object 
will be magnified to 10 X 6=60 times. With such a telescope 
the image will be formed inverted with respect to the object; but 
as it is only used, as its name implies, for surveying celestial 
bodies, this defect is of no importance. 

250. The terrestrial telescope invented by A. de Rheita, differs 
from the preceding in being furnished with two additional eye- 
pieces, so that it has in all four glasses ; and thus the images of 
objects appear erect, and the instrument is adapted for viewing 
ships, buildings, &c. 

251. The effect of common lenses in producing spherical and 
chromatic aberration, and the consequent imperfections of such 
telescopes as those just described, have been already pointed out ; 
as also the methods of correcting such errors, with reference to 
the principles on which achromatic lenses are constructed ; and 
therefore the subject need not here be further noticed. For the 
description and developement of the properties of various modifi- 

What name was given to the original instruments ? 
What is the simplest form of the instrument? 
Represent this by a diagram. 

How will the magnifying power of the simple telescope be computed f 
How will the image be situated with respect to its object ? 
How does the terrestrial telescope differ from the celestial ? 
What is the purpose of the two additional glasses in this instrument ? 
2 M 2 



414 optics. 

cations of dioptrical telescopes, we must refer the reader to the 
works mentioned at the end of this treatise. 



II. REFLECTING TELESCOPES. 

253. Newton, as elsewhere stated, despairing - of the discovery 
of a method of forming achromatic lenses, directed his attention 
to the improvement of the catadioptric telescope, invented by 
Professor James Gregory, in which an image formed by means 
of a concave mirror, or speculum, is viewed, after a second reflec- 
tion, through a convex lens or eye-glass. 

A 




254. The preceding diagram shows the general construction 
and effect of the Newtonian reflecting telescope, in which the 
concave metallic speculum C D receives the rays issuing from the 
object A B, which it renders convergent, and thus forms a revers- 
ed image in the plane mirror E F, inclined at an angle of 45 de- 
grees; and this image being reflected to d c, at the focus of the 
lens or eye-glass G H, is seen through the aperture before it by 
the observer. 

254. In the original or Gregorian telescope, the image is viewed 
by looking towards the object, as in the refracting telescope ; and 
there are other modifications of this instrument, as those of Casse- 
grain and Herschel ; for descriptive notices of which the works 
mentioned at the end of the treatise may be consulted. 

T7ie Camera Obscura. 

255. The manner in which images may be formed in a camera 
obscura, or darkened chamber, has been already described; but 
there is an instrument in a portable form, and adapted for immedi- 
ate use, which bears the same designation, as its effects depend 
upon the application of the same principle to practice. There are 
also various modifications of the portable camera obscura, among 
the more convenient of which is that represented in the annexed 
figure. 

What led Newton to the examination and improvement of the Gre- 
gorian telescope ? 

What is the nature of that instrument ? 

Explain the diagram relating to the Newtonian modification of Grego- 
ry's instrument. 

How is the portable camera obscura constructed ? 

What is employed as a screen to receive the images in this appa- 
ratus ? 



THE MAGIC LANTERN*. 



415 




256. It consists of a square box A, 
with a circular aperture in front, 
into which is fitted a short tube, a, 
having- at its extremity a convex 
lens. This tube is made to slide 
backward or forward, so that it may- 
be adjusted to the proper point for 
near or distant objects. Then the 
rays Q P, proceeding from any ob- 
ject passing through the lens, will form an inverted image in the 
posterior focus of the lens, which being received on a reflecting 
mirror E, inclined at an angle of 45 degrees, will be thrown on a 
plate of ground glass at the top of the box. The image thus formed 
may be traced on the rough surface of the glass, by a black lead pen- 
cil or crayon of red French chalk, and afterwards taken off on paper ; 
or the figures may be drawn on tracing-paper placed on the ground 
glass, through which they will be readily perceptible. The lid of 
the box, X, has two side wings, which being raised when the in- 
strument is in use, will exclude the superfluous light, and thus 
render the images distinct. 

257. The camera lucida, invented by Doctor Wollaston, is an 
instrument analagous in its effects to the preceding, but of smaller 
dimensions, and therefore more convenient for many purposes, as 
for delineating distant objects, and for copying or reducing draw- 
ings. It consists essentially of a quadrangular glass prism, by 
which the rays from an object are twice reflected, and thus form 
an image on a plane placed below it. The prism is fitted horizon- 
tally to an axis on which it turns, so that it may be placed in a 
proper position ; and the brass frame of the instrument has usually 
two lenses adapted to it, a concave and a convex one, the former 
to be used by short-sighted persons, and the latter for long-sights. 
There are various improvements and modifications of the camera 
lucida, the best of which appears to be that contrived by Signor 
Amici. 



The Magic Lantern. 

258. As an amusing as well as instructive optical machine, 
there is hardly any superior to the magic lantern, invented by 
Father Kircher. It is composed, as shown in the margin, of a 
square tin box, containing a lamp, behind which is placed a 
metallic concave reflector ; and in front of the lamp is a plano- 
convex lens, which receives on its plane surface the reflected light 
of the lamp, and concentrates it on the object, which is mag- 



How may the images be made permanent ? 

What purpose is effected by the lid and its sectoral side-pieces repre- 
sented in the figure ? 

What are the essential parts of Wollaston's camera lucida ? 
By whom was the magic lantern invented ? 
What is the purpose of the mirror in this apparatus ? 
Which lens magnifies the image in this instrument ? 



416 



OPTICS. 



/r\ 




nified by another lens fitted 
to the extremity of a tube 
projecting from the lantern. 
The objects are painted on 
thin plates of glass, which 
may be passed through a 
narrow opening in the tube 
between the two lenses. 
This tube must be double 
one end moving within the 
other, so that the tube car- 
rying the outer lens maybe 
drawn backward or forward, 
till the object is in the con- 
jugate focus of that lens. Then if it be turned toward a vertical 
screen, a magnified image will be formed; and the further the 
lantern is withdrawn from the screen, the larger will the object 
appear ; but when the distance is considerable it becomes indis- 
tinct. 

259. Several years ago an exhibition took place, conducted by 
M. Philipsthal, and called the Phantasmagoria,* resembling in the 
general principle on which it was founded, the magic lantern, bat 
rendered more imposing, by having the objects painted on a larger 
scale, and the figures being projected on a transparent curtain of 
gummed taffeta, by which the machinery was concealed from the 
spectators. Images to represent ghosts, skeletons, and other ob- 
jects, singular or appalling, were thus displayed, and for a time 
formed an attractive source of popular amusement.f 

The Solar Microscope. 

260. This instrument differs from the magic lantern principally 
in the nature of the objects exhibited by it, and the manner in 
which they are illuminated. This purpose is effected by admitting 
the rays of the sun into a darkened room, through a lens placed in 
an aperture in a window-shutter, the rays being received by a 
plane mirror fixed obliquely, outside the shutter, and thrown hori- 
zontally on the lens. The object is placed between this lens and 

On what are the objects painted ? 

What is the necessity for a sliding-tube in the magic lantern ? 

On what circumstance will the size of the image depend ? 

In what respects did Philipsthal's phantasmagoria differ from the 
magic lantern ? 

How are objects illuminated in the solar microscope ? 

By what means are the sun's rays rendered horizontal for toe. purpose 
of this exhibition ? 

* From the Greek ^ai/Ta^*, a spectre, and '«Ay;p», an assembly. 

+ See Young's Lectures on Natural Philosophy, 1807, vol. i. ; Brews- 
ter's Natural Magic ; and likewise the Repertory of Arts and Manufac- 
tures, First Series, No. 95, in which is a copy of the specification of the 
phantasmagorian machinery, for which M. Philipsthal took out a patent. 



WORKS IN THIS DEPARTMENT. 417 

another smaller lens, as in the common microscope; and the mag-- 
nified image thus formed is to be received on a screen, as in the 
case of the magic lantern. The mirror is sometimes kept in its 
due position to reflect the sun's rays in a constant direction by a 
species of clock-work called a heliostat. 

261. Mr. George Adams, an eminent optician, invented an in- 
strument, which he called the lucernal 7>iicroscope, so constructed 
as that objects could be illuminated by the light of the lamp; and 
thus the microscope could be used at any time, or in any situation. 
An improvement on this mode of displaying highly magnified im- 
ages of minute objects has recently been adopted, by employing 
the splendid light produced by the combustion of oxygen and 
hydrogen gases on lime ; and instruments have been fitted up for 
public exhibition, presenting some of the most curious and inter- 
esting phenomena with which optical science has made us ac- 
quainted. 

How can the beam of solar light be kept steadily on the object, since 
the sun is itself apparently in motion ? 

What is the peculiarity of the lucernal microscope ? 

How is the oxy-hydrogen blow-pipe applied to microscopic exhibitions? 



Works in the department of Optics. 

Powell's Treatise on Experimental and Mathematical Optics. 
Oxford. 1833. 

Cambridge Physics, treatise on Optics, by Prof. Farrar. 

Brewster's Treatise on Optics, with an Appendix by Professoi 
Bache. Philadelphia edition, 1833. 

Library of Useful Knowledge, treatise on Optical Instruments 

Brewster's Treatise on New Philosophical Instruments, 

Coddington's Treatise on Optics, part ii. 

Loyd on Light and Vision. 

Herschel's Treatise on Light. 

Biot Traite de Physique, torn, iv 



ELECTRICITY. 

"•. Ajv*ong tni pi ysical sciences, there is, perhaps, no other so 
immediately and completely the result of the researches of modern, 
and especially of contemporary philosophers, as Electricity. It 
is true that the ancients were acquainted with one of its grand 
characteristic phenomena, namely, the property which some bodies, 
under certain circumstances, possess of attracting- various other 
bodies. Thus Plato, Theophrastus, Dioscorides, Pliny the El- 
der, and other Greek and Roman writers, state that Amber* may 
be made, by rubbing it, to attract very light substances, much 
in the same manner as the loadstone attracts iron. They were 
even aware that a similar property belongs to jet, belemnite, the 
emerald, jasper, and some other precious stones. f And notices 
occur in the writings of the ancients concerning other natural 
phenomena now known to depend on electricity ; but all these 
are reported as isolated facts, which they never referred to a com- 
mon cause, nor proposed any theory to explain and illustrate them. 

2. The first attempt towards a generalization of phenomena 
which had been so long before observed, and to so little purpose, 
was made towards the end of the sixteenth century, by Dr. Wil- 
liam Gilbert, a physician who wrote a very curious and original 
treatise on the Magnet, and being led by analogy to make experi- 
ments on the attractive property of amber, he found that the power 
it possessed of attracting light substances, was one which might 
be induced by friction in several other bodies; and he therefore 
regarded it as originating from a common cause. 

3. In the following century the subject was further investigated 
by Boyle, Otho Guericke, Sir I. Newton, and others ; but though 
they accumulated facts, they were not such as were of a nature 
on which to found general principles ; and what was known of 
electricity by no means deserved the appellation of science. 

4. In the early part of the last century, Dr. Hauksbee, a phy- 
sician, made many electrical experiments, from which he ascer- 
tained that glass was a substance in which the property of electric 
attraction could be most readily excited by friction ; and that some 
other bodies, especially metals, treated in the same manner, mani- 
fested no electric power whatever. 

What fact concerning electricity appears to have been known to the an- 
cients ? 

From what does the science derive its name ? 

In how many substances had the ancients observed electrical properties ? 

Who first attempted a generalization of electrical phenomena ? 

What names occur among the cultivators of electricity in the seven- 
teenth century ? 

* From HKsxrpov, the Greek name of Amber, the term Electricity is 
derived. 

* V. Musschenbroek Institutiones Physicse, 1748, 8vo, pp. 198, 199. 

418 



ELECTRIC PHENOMENA. 419 

5. But the grand discovery, which led to the classification of 
all material bodies under two divisions, as being either conductors 
or non-conductors of electricity, was made by Mr. Stephen Grey, 
a pensioner at the Charterhouse, London, who died in 1736. This 
gentleman, having - occupied himself with various experiments, 
partly suggested by the researches of Hauksbee, in attempting to 
ascertain how far the electric influence could be propogated verti- 
cally by means of a line connecting- two bodies, found that when 
an ivory ball was suspended from an electrified glass tube, by a 
silk cord, the electric influence would be distinctly manifested 
by the ball at the alstance of more than 700 feet ; but when a 
metal wire was used to suspend the ball, it gave no signs of elec- 
tricity whatever. 

6. It likewise appeared that glass, horsehair, amber, and resin, 
as well as silk, and in general all those bodies which can be ren- 
dered electric by friction, also possess the property of insula- 
tion, or preventing the escape of electricity; while metals, wood, 
linen, and water, have no such effect, suffering electricity to escape 
through them into any other bodies with which they may come 
in contact. 

7. It had been previously observed that light was often given 
out in the passage of electricity from one body. to another through 
the air, when, in 1744, Dr. Ludolf, of Berlin, discovered that 
ether could be set on fire by sparks produced by friction from a 
glass tube : and in 1746, the discovery was accidentally made at 
Leyden, that the electric influence could be accumulated in a bot- 
tle partly filled with water; and, by making a communication 
between the water and exterior surface of the bottle, what is termed 
an electric shock might be communicated : whence a bottle or jar 
with a metallic coating, which has the same effect with water, 
has been termed the "Leyden Phial." 

8; These discoveries led the way to those of Dr. Franklin, who 
experimentally ascertained what had been before conjectured, that 
lightning is an electrical phenomenon. The mode in which he 
conducted the investigation was by raising a kite, during a thun- 
der-storm, in June, 1752, and having attached a key to the lower 
end of the hempen string, and insulated it by fastening it to a 
post by means of silk, he found that when a thunder-cloud had 
appeared for some time over the kite, electricity was received by 
it and conveyed through the string to the key, which gave out 

Who first divided bodies into conductors and non-conductors ? 

By what experiments was Grey led to his great division of natural 
bodies? 

Enumerate the bodies of each class as he arranged them. 

How early was it discovered that electricity might inflame combusti- 
bles ? 

When and where was the principle of electrical condensation disco- 
vered ? 

What name was given to the apparatus by which it was effected ? 

Who discovered the identity of lightning and electricity ? 

Describe the manner in which this was effected. 



420 ELECTRICITY. 

electric sparks, on the knuckles of the hand being presented to 
it. Science is also indebted to Franklin for the construction of a 
theory to account for the phenomena of electricity, which, with 
some modifications, is still regarded as affording the most satis- 
factory mode of explaining them. 

9. The exhibition of phenomena apparently depending on elec- 
tricity, by the voluntary action of animals, in the case of the tor- 
pedo and some other fishes, which communicate a kind of electric 
shock to those who touch them, had long been known, when Gal- 
vani, professor of anatomy at Bologna, in 1790, observed that the 
contact of metals with the nerves and muscles of a frog, recently 
killed, produced convulsive motions, which might, for some time 
after the death of the animal, be renewed at pleasure, by repeating the 
application of the metals. These singular phenomena, with others 
of an analogous kind, were at first supposed to depend on some 
peculiar action of metals and some other bodies on the nerves of 
animals ; and regarded as constituting the foundation of a new 
science, to which, in honour of the original discoverer, was ap- 
propriated the appellation of Galvanism. 

10. Some philosophers, noticing the apparent connexion of these 
appearances with the benumbing power of the torpedo, and the 
relation that seemed to exist between the effects and those arising 
from electricity, ascribed the former to some peculiar modification 
of the electric influence, to which they gave the designation of 
animal electricity. However, the important discovery by Pro- 
fessor Volta, of Pavia, of the electric effect of certain arrange- 
ments of different metals, forming what has been since called a 
voltaic pile, and sometimes a Galvanic pile, and that of the simi- 
larity of the effect of electricity accumulated from bodies excited 
in the usual manner by friction, with the effect of such a pile, in 
causing the chemical decomposition of water and metallic oxides, 
contributed to the introduction of more correct views of the na- 
ture of electrical and galvanic phenomena, as all depending on 
the various operation of the same causes, and as belonging to the 
same science. 

11. Among the latest discoveries in natural philosophy are cer- 
tain singular and important facts which afford grounds for extend- 
ing the theory of electricity so as to include the rationale of all 
those phenomena previously regarded as belonging to the separate 
science of magnetism, which, however, from its connexion with 

What did Franklin effect for the general explanation of electrical phe- 
nomena ? 

What knowledge of electric action excited by animals had preceded 
the discoveries of Galvani ? 

How early did this philosopher make his grand discovery ? 

In what elementary facts did that- discovery consist ? 

What name was at first applied to the phenomena observed by Galvani ? 

What investigations led to the change of views in regard to the true 
nature of Galvanism ? 

What has the science of electricity been of late years extended to com- 
prize ? 



THEORY OF ELECTRICITY. 421 

the art of navigation, and its application to practical purposes, 
will form in some measure a distinct subject of investigation. 

12. The term electro-magnetism has been adopted to designate 
this class of phenomena ; and that of electro-chemistry has been 
used with reference to the effect of the electric influence on the 
chemical composition of bodies: the manner in which bodies are 
affected by the irregular distribution of heat, inducing in them or 
dissipating electricity or magnetism, has been made the subject 
of research, and provided with a peculiar appellation, in that of 
thermo-electricity ; there seems also to be some mysterious con- 
nexion between the electric or magnetic influence and light: so 
that it must be obvious that the science of electricity affords a 
most extensive field for research ; and that it is so intimately con- 
nected with other branches of natural philosophy, as to claim the 
closest attention from those who are interested in the progress of 
physical science. 

13. Within the limited space to which this sketch is restricted, 
it will be impossible to attempt more than a cursory view of the 
most striking and essential phenomena of electricity or electro- 
magnetism, with a few illustrative experiments and observations 
which may furnish correct ideas of the present state of our know- 
ledge, and enable the young inquirer to study with advantage 
works of greater extent and deeper research. 

14. Electricity may be investigated under several points of view. 
1. With reference to the sources of electric influence. 2. With 
respect to its cause, including the developement of the hypothe- 
sis of electric fluids, and the properties ascribed to them. 3. The 
distribution of the electric fluid in bodies imbued with it. 4. The 
action of electrified bodies on those which are in their natural state ; 
and the phenomena of accumulated electricity. 5. The production 
of electricity by the contact of different substances ; or, Galvanic 
electricity. 6. The production of electricity by heat; or, thermo- 
electricity, 7. The phenomena of electric currents ; or, electro- 
magnetism. 

15. To these might be added several other heads of inquiry, as 
regarding the effect of electricity on the living bodies of animals, 
in health or disease ; the investigation of the natural electricity of 
marine animals, as the torpedo and gymnotus electricus; the 
chemical effects of electricity ; and the nature of atmospheric 
electricity, or the causes of lightning, hail, the northern lights, and 
other meteorological phenomena. 

The Fundamental Properties or Mode of Action of the Electric Fluid. 

16. Some of the usual effects of electric influence, such as the 
attraction of light bodies by glass tubes excited by friction, the 

What is meant by the terms electro-magnetism and electro-chemistry!* 
What is meant by the term thermo-electricity ? 
Under how many and what aspects may electricity be regal etc** 
What incidental inquiries are. connected with its main branches ol i>» 
vestigation ? 

2 N 



422 ELECTRICITY. 

production of sparks of fire under certain circumstances, and other 
phenomena, have been mentioned as owing their origin to a com- 
mon cause, the investigation of which forms the subject of that 
branch of natural philosophy, constituting the science of electri- 
city. Like the essential causes of light and heat, that of electri- 
city can only be inferred from observation and experiment. 

17. But in order to trace with accuracy the operations of this 
powerful agent, and elucidate its mode of action, some hypotheti- 
cal principle may be advantageously assumed, by means of which 
the phenomena may be connected and accounted for, as resulting 
from its influence under any given circumstances. Hence the 
existence of an ethereal fluid, either identical or analagous with 
that on which depend the phenomena of light and heat, may be 
admitted ; and the term electricity or electric fluid may be em- 
ployed to designate it. 

18. But we should carefully avoid considering it as a palpable 
form of matter, the existence of which can be directly demon- 
strated. Instead of which, it should be regarded as merely a con- 
venient method of explaining certain appearances, and showing 
their mutual relations, so that we may be enabled to contemplate 
them in connexion with each other. 

19. Dr. Franklin advanced a theory of electricity by means of 
which he accounted for the phenomena as depending on the ac- 
tion of a particular fluid, existing in all bodies, and of which each, 
according to its capacity, possessed a relatively greater or smaller 
quantity. When this fluid is in a state of equilibrium, or equally 
distributed among two or more bodies in communication with each 
other, it is quiescent, and no particular effects are perceived ; but 
if the equilibrium be destroyed, as by the contact of a body in a 
different electrical state, a new distribution takes place, and vari- 
ous phenomena rmj arise from the passage of electricity from one 
body to another. Thus ihe phenomena were supposed to depend 
on the excess or defect of the electric fluid; those bodies which 
were overcharged with it having a tendency to impart it to others, 
and those in which it might be less abundant to receive it. 

20. It further appeared that bodies in a similar state of electri- 
city, whether of excess or deficiency, always attracted each other ; 
while bodies similarly electrified constantly repelled each other ; 
the terms positive and negative electricity were therefore adopted to 
designate the states of bodies as to the quantities of electric fluid 
contained in them; those in which it was supposed to exist in 

How can we arrive at a comprehension of the cause of electrical phe- 
nomena ? 

What assumption is it necessary to make in speaking of electric action ? 

How are we required to restrict the meaning of the term electric fluid? 

What supposition was adopted by Dr. Franklin lo account for electrical 
effects ? 

What was meant by electrical equilibrium, according to that theory ? 

What obvious phenomenon was observed to occur between bodies in the 
two opposite states ? 

When was a body said to be positively electrified ? when negatively ? 



POSITIVE AND NEGATIVE ELECTRICITY. 423 

excess being termed positively electrified bodies, and those in 
which the quantity was relatively deficient negatively electrified 
bodies. 

21. This theory accounts satisfactorily for some of the most 
important phenomena, but there are others to which it appears 
to be inapplicable ; in consequence of which, though once gene- 
rally received, it is now almost entirely abandoned, and has been 
replaced by an hypothesis originally proposed by Mr. Symmer, 
an American philosopher, who ascribed the appearances observed 
to the existence of two kinds of electric fluid, and their separate 
or united influence under various circumstances. 

22. According to this system all bodies in nature contain elec- 
tric fluid ; and the earth itself is to be regarded as an immense 
reservoir of electricity. This fluid is supposed to consist of a 
combination of two distinct ethereal essences, which neutralize 
each other; and it is only when they are separated that electrical 
phenomena are observed. They may be separately collected, and 
thus made to display their distinct properties; but they manifest 
a strong disposition to reunite, and it is principally at the instant of 
reunion that the most striking appearances are exhibited ; for their 
combination paralyzes their several powers, and the compound 
fluid becomes perfectly quiescent and ineffective. 

23. To these fluids English philosophers have generally given 
the names of positive and negative fluids, borrowing in part the 
phraseology of Franklin. In France, however, the former has been 
termed the vitreous fluid, because it is that which is commonly 
produced by the friction of glass ; and the latter has received the 
designation oi resinous fluid, as it is in the same manner exhibited 
by the friction of resin or sealing-wax : though, as will be subse- 
quently shown, the positive or vitreous fluid may be rendered 
active by rubbing resin, and the resinous fluid on the contrary 
produced from the friction of glass; the effects depending partly 
on the nature of the substances applied to the glass or resin re- 
spectively, and being modified by the relative temperature of 
bodies, and other circumstances. 

24. One of the most simple yet at the same time important 
experiments to show the effect of bodies in different states of 
electricity may be performed by means of a glass tube, about 
three feet in length, and three-quarters of an inch in diameter; on 
rubbing which with a dry silk handkerchief, it will become ex- 
cited with positive electricity; and if a light downy feather, quite 
clean and dry, suspended from a silk thread, be held near the 

How does the system of Symmer differ from that of Franklin ? 

What tendency have the two opposite electricities in regard to a neu- 
tral condition ? 

What names do English writers commonly apply to the two electrici- 
ties p 

What terms are in use in France and other countries on the continent 
of Europe ? 

What experiment demonstrates the effect of oppositely electrified ho- 
dies ? 



424 ELECTRICITY. 

tube, it will be immediately attracted and adhere to it; but if it 
be then withdrawn, still held by the silk line, and not suffered to 
come in contact with any other body, it will be found, on again 
bringing it near the tube, to be repelled, instead of being attracted 
as before. 

25. These appearances are to be explained, as depending on 
the feather having been imbued with negative electricity in the 
first instance, and therefore becoming attracted by the positively 
electrified tube, which having communicated a portion of its 
electricity to the feather, sufficient to neutralize its former electri- 
city, and bring it into the positive state, both bodies become 
similarly electrified, and therefore mutual repulsion takes place, 
manifested by the feather, as being by far the lighter body, flying 
off from the tube. 

26. Let a large stick of red sealing-wax be rubbed with dry warm 
woollen cloth, and it will be perceived that the suspended feather 
presented to it will be first attracted and then repelled, as in the 
former case. But if the feather, after having been positively 
electrified by contact with the excited glass tube, be presented to 
the sealing-wax, it will not be repelled, as it would be by the 
tube, if again presented to it, but would be more strongly attracted 
by the sealing-wax, than when in its natural state, plainly de- 
monstrating that since it has been positively electrified by the 
glass, the sealing-wax which now attracts it must be in a nega- 
tive state. This experiment may be reversed by presenting the 
feather in its natural state to the excited sealing-wax, and then 
bringing it near the glass tube, by which it would be instantly- 
attracted ; for having been negatively electrified by contact with 
the sealing-wax, it attaches itself to the positively electrified tube. 

27. It has been observed that whenever electricity is excited 
by the friction of one body against another, both kinds are pro- 
duced, the one body becoming negatively, and the other positively 
electrified. Thus when glass is rubbed by silk or flannel, nega- 
tive electricity is excited in the rubber, while the glass becomes 
positive; and if sealing-wax or resin be rubbed with flannel or 
woollen cloth, the negative electricity excited in the resin or wax 
will be accompanied by the developement of positive electricity 
in the woollen. Polished glass acquires positive electricity from 
friction with almost all substances except the back of a cat, which 
renders it negative ; but if ground glass be rubbed with silk or 
any of those substances which excite positive electricity in smooth 
glass, it will become negatively electrified, and the rubbing bodies 

In what manner is the experiment to be explained ? 

What difference in the electric state of a light insulated body will be 
manifested after touching' it with excited sealing-wax, from that which 
arises from the use of a gkss tube ? 

What two effects must always be produced when two bodies are rubbed 
together to produce electricity ? 

Enumerate some of the substances which, when used together, take op- 
posite electrical states. 

What substance may render polished glass negative ? 



CONDUCTORS AND NON-CONDUCTORS. 425 

will be positively electrified . So sealing-wax, when rubbed against 
an iron chain, if the surface of the former be smooth, it will be 
excited with negative electricity ; but if its surface be previously 
roughened with scratches, it will become positively electrified. 

28. Hence it appears that the excitement of one kind of electri- 
city or the other depends much on the surfaces of bodies; and 
therefore it may be conceived that the electric fluid is chiefly dis- 
posed on the external parts of solid bodies. As two surfaces 
rubbed against each other acquire opposite kinds of electricity, it 
might be expected that they would attract each other, and that is 
always found to be the case. If a black and a white ribbon, each 
about a yard in length, and perfectly dry, be applied together, and 
then drawn several times between the finger and thumb, so as to 
rub against each other, they will be found to adhere, and if sepa- 
rated by pulling one end from the other, they will fly together 
again. While they remain united they manifest no sign of elec- 
tricity; for being in opposite states, they neutralize each other; 
but if completely separated, each will exhibit its peculiar electri- 
city, those bodies being attracted by the one ribbon which are 
repelled by the other. 

29. When the experiment is made in a dark room, flashes of 
light are perceived from the surfaces of the ribbons, together with 
a rustling noise. The black ribbon in this case will be found to 
be negatively electrified, and the white ribbon positively. By 
taking ribbons from the same piece and of equal length, and draw- 
ing one of them lengthwise at right angles across the other, the 
former will acquire positive and the latter negative electricity. 
The friction of liquids or gases against solid bodies will excite 
electricity ; and the effects of contact, pressure, or friction of any 
one body against another will in some degree produce the same 
effect, the appearances being variously modified according to cir- 
cumstances. 

30. The following substances become positively electrified if 
rubbed with either of those mentioned after them, and on the, 
other hand when one of these substances is rubbed with either of 
those named before it, the substance rubbed becomes negatively 
electrified: 1. The back of a cat. 2. Polished glass. 3. Wool 
and woollen cloth. 4. Feathers. 5. Dry wood. 6. Paper. 
7. Silk. 8. Gum lack. 9. Ground glass. 

31. It has been already stated that some kinds of substances 
freely transmit electricity to bodies in contact with them, or suffer 
it to escape through them ; while others retain it, or prevent its 

On what does the particular state which any body shall take, when 
rubbed, appear to depend ? 

How may the developement of electricity by differently coloured rib- 
bons be exhibited ? 

Why will not two pieces of" silk, when oppositely electrified and placed 
together, show signs of electricity ? 

How may liquids and aeriform bodies be made to excite electricity . ? 

State the order in* which the several electrics become either positive or 
negative according to the substance with which they are rubbed. 
• 2 n 2 



423 ELECTRICITY. 

passage : the former are named conductors of electricity, and the 
latter non-conductors. 

32. Among 1 solid bodies, the metals are generally excellent con- 
ductors, and yet they appear to be very unequal as to their powers 
of conduction; linen, straw, and wood charcoal are likewise good 
conductors; while glass, resins, sulphur, silk, wool, sugar, fat, 
and various other substances are either non-conductors, or possess 
the conducting power in a very imperfect degree. Most kinds of 
wood when quite dry, and animal fibres deprived entirely of the 
juices they naturally contain, become nearly absolute non-conduc- 
tors ; but in their fresh state they conduct electricity freely, doubt- 
less inconsequence of the liquid matter with which they are pene- 
trated. Hence the bodies of men and other animals suffer the 
electric fluid to pass through them with great facility. 

33. All liquid substances, except fat oils, are good conductors, 
though not equally so ; for essential oils, and spirit of wine do 
not conduct electricity so readily as water ; and the latter fluid 
has its conducting power augmented by combination with aeida 
or saline substances. 

34. Air and all gaseous fluids, when free from moisture, are bad 
conductors, and the more dense they are the greater will be their 
resistance to the passage of electricity through them. Atmos- 
pherical air, therefore, in dry weather becomes a non-conductor; 
but when charged with moisture, as from a fog, the electric fluids 
traverse it more readily. Temperature also, as might be concluded, 
influences its conducting power, which is greatly augmented by 
heat. 

35. Those bodies which are good conductors of the electric fluids 
may be excited by friction as well as the non-conductors, but the ef- 
fects produced will depend on the circumstances in which they are 
placed. Thus a cylinder of brass, or any other metal, grasped by 
the hand, if rubbed with silk or flannel, will be perfectly inert, not 
displaying any attractive power, like rubbed glass or sealing-wax, 
when brought near to a light feather. But if a handle of baked 
wood or glass be fixed to a metal cylinder, so that it may be held 
without touching the cylinder itself, and the latter be rubbed with a 
dry silk handkerchief, or piece of flannel, it maybe readily excited, 
generally manifesting negative electricity, and it will act on the 
feather accordingly. In such a case the electricity is prevented 
from passing off from the metal, through the body of the person who 



What gives rise to the distinction of bodies into conductors and non- 
conductors ? 

What bodies are among the best conductors ? 

What are some of the bodies which may change their character ac- 
cording to the state in which they happen to be tried ? 

What liquids are bad conductors of electricity ? 

What power of conduction has dry air ? 

What influence has heat on the conducting power of air ? 

Under what circumstances may a metallic cylinder be excited by rub- 
bins: ? 



INDUCTION OF ELECTRICITY. 



427 



holds it, by the insulating" or non-conducting handle of dry wood or 
glass. 

36. From the power which the most perfect non-conductors 
possess of preventing the escape of the electric fluids from con- 
ductors supported by them, they have been termed insulators, and 
as they most readily exhibit electricity by friction, they have also 
been called electrics, while the appellation of non-electrics has been 
applied to the metals and other freely-conducting substances. 
These terms, however, can hardly be considered as correct, since 
bodies differ more essentially in their power of retaining electri- 
city than in their capacity for receiving it ; and hence the more 
obvious distinction between conductors and non-conductors. 

37. In making experiments relative to the accumulation or trans- 
fer of the electric fluids, it is necessary to use instruments so con- 
structed as that a conducting body may be supported and thus in- 
sulated by means of a non-conductor. On this principle is formed 
that necessary part of electrical apparatus called the prime conduc- 
tor, usually consisting of a brass cylinder fixed horizontally by 
one or more rods or thick tubes of glass to a wooden stand. 

38. It may be inferred from the experiment with a glass tube 
and an insulated feather, that any body capable of free motion, on 
approaching another body powerfully electrified will be thrown 
into a contrary state of electricity ; and thus a feather brought 
near to a glass tube excited by friction is attracted by it, and there- 
fore previously to its touching the tube negative electricity must 
have been induced in it: and on the other hand, if a feather he 
brought near excited sealing-wax it will be attracted, and conse- 
quently positive electricity must have been induced in it before 
contact. Hence it appears that electricity of one kind or the other 
is generally induced in surrounding bodies by the vicinity of a 
highly excited electric. This mode of communicating electricity 
by approach is styled induction. 

39. When an electrified body thus causes electricity in another 
by induction, the effect extends only to that part of the surface 
of the latter body immediately opposite to the former, while the 
other extremity will exhibit a contrary state of electricity. 

This may be shown 
C 



D 



by means of a brass 
wire A, in the annexed 
figure, moving freely on 
a pivot, and supported 
by a glass tube E ; and a 
brass cylinder or con- 
ductor B, similarly sup- 
Whence 1ms the term insulator been derived ? 
To what is electric applied ? 

How are we to arrange conductors and non-conductors for the purpose 
of showing the accumulation of electricity? 

Into what electrical state is any body brought by being placed near one 
which has already been electrified ? 
How is this exemplified P 



428 ELECTRICITY. 

ported, and placed within a few inches of the extremity of the 
wire C, carrying- a small ball of pith of elder. 

40. If the conductor be positively electrified, the ball C will 
become negative, as may be shown by approaching- to it an ex- 
cited stick of sealing-wax, by which it will be repelled ; while 
the ball D will be attracted by the sealing--wax, and must there- 
fore be in a positive state of electricity. In this case the wire A 
is said to be in an eledro-polar state, having a negative pole C op- 
posite to the positively electrified conductor, and a positive pole 
D, at its opposite extremity. Such an arrangement might be car- 
ried to any extent. Thus if another brass wire similarly insulated 
and armed with pith balls were to be placed near the extremity D, 
the ball opposite to it would be negatively electrified, that at the 
other end positively, and so on. 

41. The instrument above described, or mounted brass wire 
with its balls, forms a convenient electroscope,* to indicate the 
electrical states of bodies ; and as such it was proposed by the 
French philosopher, Hauy. On the same principle depends the 
action of the more simple electroscope, consisting of two small 
pith balls suspended by a fine linen thread or silver wire to the 
extremity of an insulated conductor. When such an instrument 
is electrified, the two balls necessarily acquiring the same kind of 
electricity will separate from each other ; and the nature of their 
electricity may be ascertained by presenting to them an excited 
glass tube, which, if they are positively electrified, will make 
them more divergent, if negatively will draw them nearer ; and 
with a stick of excited sealing-wax, the reverse effects would take 
place. 

42. A more delicate instrument for estimating the kind of elec- 
tricity is that called Bennet's gold-leaf electrometer, composed 
of two small slips of gold leaf suspended within a glass jar, which 
by their divergence or collapse on the approach of an electrified 
body to a brass ball connected with them by a wire passing through 

\the neck of the jar, indicate that its electricity is similar or con- 
trary to that of the gold leaves. An arc of a circle graduated 
may be so placed as to show the relative extent of the divergence of 
the leaves, according to the degree of electricity in the body pre- 
sented to the electrometer. 

43. Another very delicate electrometer is that called the electric 
balance, invented by M. Coulomb ; in which the force of electri- 

Wbat name is given to this mode of exciting electricity ? 
In what state are the opposite ends of a conductor thus electrified ? 
Describe the apparatus by which this effect is demonstrated. 
In what state is the body electrified by induction said to be ? 
Can a body electrified by induction communicate an electrical excite- 
ment to another insulated body ? 

What use did Hauy make of the wire and balls insulated on a pivot ? 
What other similar apparatus depends on the same principle ? 
Describe Bennet's gold-leaf electrometer. 

* From the Greek HxsxTpoi-, (see p. 418), and ivosrew, to observe. 



ELECTRICAL MACHINE. 



429 



eal repulsions and attractions, is measured by the torsion of a 
wire; and others have been contrived, by means of which the 
amount of electric repulsion may be ascertained and measured on 
a graduated scale. From experiments with the electric balance 
it has been concluded that the influence of electricity, like that 
of gravitation, is in the inverse ratio of the squares of the distances 
of the acting" bodies ' 



Electrical Instruments and Experiments. 

44. Electricity is usually developed, in order to show its effects, 
by the friction of glass. The earlier electricians, in the prosecu- 
tion of their researches, merely used glass tubes or other non- 
conductors, held in one hand and rubbed with silk or flannel. 
Dr. Hauksbee made an improvement on this tedious process, by 
arranging a glass globe so that it might be made to revolve con- 
tinually on an axis; and Professor Winkler of Leipsic, contri- 
buted greatly to render the apparatus useful and convenient, by 
affixing a cushion of soft leather stuffed with horsehair, so that by 
the pressure of a spring it might rub against the revolving globe. 

45. Such an arrangement as that just described constitutes an 
electrical machine ; but subsequent experimentalists have made 
many alterations; and among the most simple and yet advantage- 
ous modifications of this instrument may be reckoned that invented 
by Mr. Nairne, a mathematical instrument maker, as represented 
in the following figure. It consists of a glass cylinder, C C, from 

10 to 16 inches in diameter, 
and about twenty inches in 
length, supported, so that it 
may turn on its axis, on two 
pillars of glass, fixed to a 
wooden stand. Two metallic 
conductors, P N, equal in 
length to the cylinder, and 
about one third of its diameter, 
are fixed parallel with it, on 
either side upon two glass pil- 
lars, which are cemented into 
two separate pieces of wood, 
sliding in grooves so that they 
may be respectively adjusted 
at any distances from the cy- 
linder required. To one of 
these conductors, N, is attached a cushion an inch and a half 
wide, and about as long as the cylinder, against which it may be 
made to press by means of a bent spring; and to the upper part 

On what principle was Coulomb's torsion balance constructed ? 

How is electricity most commonly developed ? 

How was this effected by tbe early electricians ? 

What improvements were made by Hauksbee and Winkler } 

Describe the essential parts of Nairne's electrical machine. 




430 ELECTRICITY. 

of it is sewed a flap of oiled silk, which extends loosely over the 
cylinder, to within an inch of a row of brass pins or pointed wires 
proceeding from the side of the opposite conductor. The conduc- 
tor to which the cushion is attached is called the negative con- 
ductor, and the other, which by means of its points collects elec- 
tricity from the glass, is named the positive conductor, and also 
the prime conductor. The cylinder may be made to revolve, in 
the direction of the silk flap, simply by a winch fitted to it, or by 
a multiplying wheel, W. 

46. In order that the machine may be worked with the greatest 
effect, the cylinder and every other part must be made perfectly 
clean and dry ; and as may be supposed, it displays the greatest 
power when the air around it is quite free from moisture. To 
augment the efficacy of the machine, it is usual to apply to the 
cushion an amalgam of zinc and tin, made by melting together one 
part of tin and two of zinc, and mixing them in a heated iron 
mortar with six parts of hot quicksilver; and after the compound 
has been reduced by trituration to a powder, it must be made into 
a stiff paste, with pure hog's lard. 

47. When it is requisite to obtain positive electricity, the 
cushion or negative conductor must be connected with the wooden 
stand of the machine by a chain or wire ; and thus the electric 
equilibrium of the rubber is restored, by the earth, as fast as it is 
disturbed by the action of the machine; but the opposite positive 
conductor being insulated cannot return to a state of equilibrium 
except by the action of the wire. If it be required to produce ne- 
gative electricity, the cushion must be insulated by removing the 
chain, and attaching it to the prime conductor P, whence the posi- 
tive electric fluid will pass to the earth, and the conductor N will 
become negatively electrified. 

48. There is another form of the electrical machine, consisting 
of a circular glass plate, fitted up so that it may be made to re- 
volve between two rubbers. It is a powerful instrument; and, 
when properly made, is easily adapted for producing positive or 
negative electricity. In both forms of the machine the quantity 
of electricity developed in a given time will depend, other things 
being equal, on the extent of surface rubbed, and the goodness of 
the insulation by which the reunion of the two electricities can be 
prevented. The intensity or striking distance of electricity, in a 
machine of either form, must depend on the distance between the 

What names are given to the two conductors with which that machine 
is furnished ? 

What is the object of the wheels and band in this apparatus? 

What precautions are necessary to insure the efficacy of an electrical 
machine } 

What substance is applied to augment the action ? 

What adjustment of parts will yield positive electricity? 

How may the negative electricity be exhibited ? 

On what will the quantity of electricity depend, in any machine of a 
given form ? 

To what will the intensity be proportioned ? 



ELECTRICAL PHENOMENA. 431 

rubber and the collecting points, that is, in general, on the diame- 
ter jjf thcplate or cylinder.* 

49. M.. Beudant-has described a machine that has the advan- 
tage of being less costly than those of glass, and exempt from injury 
by accident. It may be constructed by taking two yards of var- 
nished taffeta, and sewing together firmly, with a flat seam, the 
two ends, so as to make it like what is called a jack towel ; and 
it is then to be stretched over two wooden rollers, one of which 
being turned with a winch, the taffeta will pass continuously over 
them, cushions of hare or cat skin being placed so as to rub against 
it; and a conductor with points may be placed near its surface to 
collect the electricity produced. f 

50. When an electrical machine, as above described, Avith a 
glass cylinder, has been properly prepared, and during a dry state 
of the atmosphere, if the cylinder be made to revolve with a cer- 
tain degree of velocity, sparks and vivid flashes of light will be 
perceived passing over the surface of the glass, from the cushion 
to the conductor; and if the knuckle be presented to the conduc- 
tor, sparks, with a sharp report, will proceed from it to the knuckle, 
causing a peculiar and slightly disagreeable, but momentary sensa- 
tion. The light is supposed to be occasioned by the sudden com- 
pression of the air, by the transit of the electric fluid; 'and it is 
accompanied by the developement of heat, for gunpowder, alcohol, 
fulminating silver, and other highly inflammable bodies may be 
set on fire by means of the electric spark. 

51. The operation of the electrical machine depends on the 
glass becoming positively electrified by friction against the rub- 
ber, when the cylinder or plate is put in motion, and the rubber 
or cushion consequently becoming negatively electrified. The 
positive electricity thus acquired- by the glass is regularly attracted 
and carried off by the metallic points of the prime conductor, in 
which it becomes accumulated. But if both conductors be insulated, 
so that the cushion connected with the negative conductor cannot 
continue to derive electricity from the earth or surrounding objects, 
it will soon cease to afford electricity to the other conductor by 
means of the glass cylinder. In order, therefore, that the supply 
may be kept up, it is requisite that either the cushion or the con- 

What construction has Beudant proposed for an electrical machine? 
What is supposed to be the cause of electrical light ? 
On what does the operation of the machine depend ? 
What takes place when both conductors are insulated r 

* For an experimental investigation of this and other subjects cor 
nected with the action of electrical machines, the reader is referred to 
the 25th volume of Prof. Silliman's American Journal of Science, p. 57. 
—En. 

t Traite Elem. de Phys., p. 570. The idea of Beudant is sometimes 
realized in the action of machinery driven by broad leather bands moving 
rapidly over pullies. As there is a considerable amount of friction, and as 
both leather and wood become dry and warm, electrical sparks may be 
obtained. — Ed. 



482 ELECTRICITY. 

d actor should communicate with the earth, or with the floor, by 
some good conducting - medium, as a metal chain or wire. 

52. Hence it appears that the electricity of either conductor 
must be extremely weak, when both of them are insulated; that 
if" one conductor alone be insulated, the power of the other will be 
proportionally augmented; that the cushion and the glass must 
alwa3^s be in opposite states, the one being positive and the other 
negative; and that the opposite electricities are exactly in that 
proportion which will cause them when combined to neutralize 
each other. The effects produced by the positive conductor, or 
that opposed to the cylinder, will be similar to those of an excited 
glass tube ; and the effects of the negative conductor, or that con- 
nected with the cushion will correspond with those of an ex- 
cited stick of sealing-wax. 

53. If two suspended pith balls be attached to either conductor, 
they will be observed to repel each other, manifesting the same 
kind of electricity ; but if one ball be attached to the positive, and 
another to the negative conductor, they will attract each other. If, 
however, the two conductors be connected by a metal rod, their 
opposite electricities will neutralize each other, and no signs of 
either state will be exhibited. 

54. Th,e passage of a spark indicates the annihilation of the 
opposite states of electricity previously existing in the bodies 
between which the spark passes, and which has been already 
shown to be the effect of induction on the approach of bodies to- 
wards each other. Thus, the knuckle, when presented to the posi- 
tive conductor, becomes negatively electrified ; and when the 
opposite electricities thus induced become sufficiently intense, the 
appearance of the spark announces that the state of excitation is 
terminated. 

55. The most important phenomena depending on the principle 
of induction are those arising from the accumulation of electricity. 
This is what takes place in using the electrical jar, or, as it has 
been termed, the Leyden phial, the property of which was acci- 
dentally discovered by Professor Musschenbroek, of Leyden, or, 
according to some writers, by M. Cuneus. Its mode of action 
may be readily exhibited by taking a glass bottle nearly filled 
with water, and placing it in a basin of water ; a chain or rod of 
metal must be passed into the bottle below the surface of the wa- 
ter, and continued from it to the positive conductor of an electrical 
machine, and another chain must have one end immersed in the 
water of the basin surrounding the bottle, and the other end trail- 
ing on the floor, or connected with the cushion. 

What will be the electrical condition of both conductors when both are 
insulated ? 

In what proportion are the opposite electricities always found ? 

What phenomenon will two pith balls exhibit when suspended to either 
conductor of the machine ? 

What does the passage of a spark indicate ? 

Ituvf may the Leyden phial, in its simplest form, be exhibited ? 



THE LEYDEX PHIAL. 



433 



6. On turning the machine, the electrical fluid received by the 
conductor will pass from it by means of the chain or rod to the 
interior of the bottle, where it will be accumulated; and in order 
to discharge it, a communication must be made between the rod 
or chain proceeding from the bottle, and that immersed in the 
basin ; and thus the confined electricity will make its escape. A 
person grasping the latter chain with one hand, and touching the 
other or the conductor with which it is connected with the other 
hand, would receive the whole charge of the phial, constituting 
what is termed an electric shock. 

57. It was in this manner that Musschenbroek undoubtedly 
became practically acquainted with the effect of accumulated 
electricity ; and the sensation he experienced so strongly impress- 
ed him that, in a letter on the subject which he addressed to 
Reaumur, he said the crown of France would be but a feeble in- 
ducement to expose himself to the hazard of receiving such 
another shock.* The sensation caused by the discharge of an 
electric jar is not, however, so formidable as might be supposed 
from the alarm of the alleged discoverer ; and unless the jar be 
large and highly charged, the shock will only occasion a momen- 
tary painful feeling, much resembling that caused by suddenly 
striking the elbow against a hard substance, but more transient. 

58. A more convenient form of the Leyden phial than that just 
described consists of a wide mouthed jar, coated outside and inside 
with tinfoil, to within about two inches of the top; having a 
wooden cover, fitted into the mouth like a cork, and pierced so 
that a strong brass wire may pass through the cover, terminating 
below in a chain in contact with the inner coating of the jar, and 
having at the other end a brass knob or ball. A jar or bottle with 
a narrow neck, as represented in the margin, may be used, but as 

in that case it can be coated only on 
the outside, it must be filled with 
some metallic substance, as mer- 
cury, or steel filings, as high as the 
coating B reaches ; or moderately 
warm water may be poured into it 
whenever it is wanted for use.f 

59. A jar may be electrified by 
placing it near the positive conduc- 
tor of a machine, with which the 
knob A must be in contact; and then, 
on turning the cylinder, the electric 
fluid will pass from the conductor 
to the jar, in which it will become 
accumulated ; and in order to dis- 
How is the discharge of the phial to be effected ? 



^ — ^fltojj 




* Libes Hist. Philos. des Prog-, de la Physique, t. ill. p. 141. 

T For a description of a convenient method of fixing a metallic coating 
to the inside of a phial, see Dr. Olinthus Gregory's Lessons, Astronomi- 
cal and Philosophical, 6th edit. 1824, p. 12". 
20 



434 ELECTRICITY. 

charge it a bent or jointed wire mast have one extremity placed 
against the outer coating of the jar, and the other being ad- 
vanced towards the knob, nearly the whole charge will es- 
cape from the inside of the jar, through the wire, to the outer 
coating. A curved brass wire, called a discharger, is sometimes 
fitted up with a knob at each end, C,D, and a glass handle; but 
the jar may be safely discharged by the bent wire only, as the 
fluid will pass wholly through it without affecting the person who 
uses it. In charging the jar care must be taken that the exterior 
coating be allowed to take the state opposite to that of the inte- 
rior. This may be perhaps most conveniently effected by con- 
necting the outside of a jar or battery when undergoing the ope- 
ration, immediately with the rubber of the machine ; then con- 
necting the prime or positive conductor with the interior the 
charging will proceed with entire success, though the jar, the 
machine, and even the person who works it be perfectly insulated 
from the ground. By connecting the rubber with the interior, 
and the positive conductor with the exterior, the battery will be 
charged internally with negative electricity. 

60. As the effect of the electrical jar will be proportioned in 
part to the quantity of coated glass it contains, and in part to the 
thinness of the glass, it must be obvious that its power will great- 
ly depend on its size. Very large jars, however, would be 
awkward, inconvenient, and liable to be broken by slight shocks 
if veTy thin, as well as highly expensive. Hence means have 
been contrived for combining any number of jars, so that they 
may be all charged at the same time, and discharged with equal 
facility as a single jar. This may be effected by forming a con- 
nection between all the wires proceeding from the interiors of 
the jars, and also connecting ail their exterior coatings; and such 
an arrangement is styled an electrical battery. The discharge of 
electricity from such a combination is accompanied by a loud re- 
port ; and when the number of the jars is considerable, animals may 
be killed, metal wires be melted, and other effects be produced by 
the discharge of the battery, analagous to those of lightning. 

61. By means of an electrical machine a vast number of curious 
and interesting experiments may be performed, a few of which 
may be here described. 

The effect of electricity in producing the divergence of tufts of 
hair is sufficiently amusing. This may be shown by placing a 
person on a stool with glass legs, so that he be perfectly insulated, 

What account did the discoverers of the Leyden phial give of their sen- 
sation on receiving the shock ? 

What form of this apparatus is roost convenient in practice ? 

How may such a jar be charged ? 

What apparatus maj r be used in the discharge ? 

On what two circumstances in the construction of a jar will its efficiency 
depend ? 

How is the necessity of using very large jars obviated ? 

What is an electrical battery ? 



ELECTRICAL EXPERIMENTS. 



435 




and making him hold in his hand a brass rod, the other end of 
which touches the positive conductor; then on turning- the ma- 
chine, the hairs of the head will diverge in all directions. The 
same effect may be more perfectly exhibited by means of an arti- 
ficial head, of small dimensions, with hair glued to it, and fixed 
on a brass wire, which is to be placed on the conductor. 

62. The electrical bells {carillon eledrique, as designated by 
the French) consist of a number of 
small bells, as represented in the annex- 
ed figure, suspended from the conduc- 
tor by brass chains, with a ball to act 
as a clapper hanging by a silk thread, 
between every two bells, one of them 
being connected with the table, so that 
its electricity is neutralized as fast as it 
is received. Thus the insulated ball 
will vibrate backwards and forwards al- 
ternately striking the electrified and non- 

,-s.rr^^r electrified bell, when the machine is put 
in motion. 

63. The dancing figures, as shown in the margin, may be cut 
out of writing paper ; and such figures, or 
any other light bodies, placed on a brass 
plate B, connected with the ground, and 
having another brass plate A, suspended 
at a little distance above it, from the prime 
conductor, will rapidly dance when the up- 
per plate is electrified. 

64. The effect is obviously caused by 
the figures being attracted by the electrified 
plate and immediately after repelled, and 
being robbed of their acquired electricity 
by the lower or non-electrified plate, they 
rise again to receive a new charge, and 
thus the dance is continued. 

65. The manner in which buildings are 
injured when struck by lightning, or the accumulated electricity of 
the atmosphere, may be instructively elucidated by means of the 
apparatus delineated in the following figure, called a Thunder- 
house. It consists of a triangular piece of mahogany, which may 
represent one end of a house or barn : in the centre a small square 
piece is fitted loosely into a corresponding cavity ; and diagonally 
across the moveable square passes a brass wire, C D. When this 
instrument is used, the brass knob A must be brought near to the 

How is the divergence of the hair, and similar effects on the person, 
produced by electrification ? 

Describe the electrical chime of bells. 

How is the electrical dance to be explained ? 

What apparatus illustrates the effect of lightning on objects which it 
encounters r 




436 



ELECTRICITY. 



knob of a charged jar, with the outside of 
which is connected a chain attached to the 
brass wire B ; thus the jar will be dis- 
charged, and its electricity will pass 
through the knob and wire A to B; 
but the interruption occasioned by the 
position of the square in the centre will 
cause it to be forcibly driven from its 
place. If, however, its position be alter- 
ed, so that the wire C D may communi- 
cate with A and B, forming a part of the 
same electric circuit, the fluid will pass 
through the wire C D without displacing the square. 

66. It is thus that the highest point or points of a building being 
struck by lightning, if the passage of the electric fluid be inter- 
rupted, by non-conducting or imperfectly conducting bodies, they 
may be displaced with violence, injured, or destroyed; but if the 
electric fluid can pass readily through a good conductor, as a thick 
metal rod, it will be conveyed into the earth without hazard of the 
safety of the building. Hence the utility of conductors affixed to 
towers and other lofty edifices. In practice, the lightning rod 
must be furnished with a sharp point instead of the ball exhibited 
at the top of the model. 




GALVANISM. 



67. The effects of electricity depending on the accumulation of 
the electric fluids by the friction of non-conducting bodies having 
been pointed out, we shall next attempt to explain those pheno- 
mena which appear to be caused by circulating currents of those 
fluids, produced by the contact of bodies in different states of 
electricity, and especially by the contact of metals and other good 
conductors. Phenomena of this nature constitute the objects of 
that branch of physical science termed Galvanism or Galvanic 
electricity, from the discoveries of Professor Galvani of Bologna; 
and sometimes Voltaism, or Voltaic electricity, from the subse- 
quent researches of Professor Volta of Pavia, who made great ad- 
ditions to our knowledge of the subject, with reference both to 
facts and theory. 

68. The earliest notice which has been observed of any phe- 
nomenon attributable to Galvanism, occurs in a work entitled " A 



In what form must the termination of a lightning rod be ? 

What is meant by galvanism ? 

From whom does that science derive its name ? 



ANIMAL ELECTRICITY. 437 

General Theory of Pleasures," published in 1767, by John George 
Sulzer, a German writer of some eminence on philology and meta- 
physical philosophy. He states that when two pieces of different 
metals are applied to the upper and under surfaces of the tongue, and 
then brought into contact, a peculiar taste will be perceived. Sulzer 
made an abortive attempt to account for this curious fact, which 
seems to have attracted no particular attention till a later period, 
when further discoveries led to the inference that it ought to be 
regarded as depending on electricity. 

69. Professor Galvani, already mentioned, about 1790, acciden- 
tally made the discovery that the transmission of a small quantity 
of electricity through the nerves of a frog, shortly after the death 
of the animal, would excite muscular contractions in its limbs. 
And he afterwards found that similar contractions could be pro- 
duced, by touching the muscles of the leg of a dead frog with one 
metal, and the nerves belonging to them with another, and then 
bringing the metals into contact. 

70. This singular effect of electricity may be experimentally 
Am*s exhibited, by preparing the hind limbs of a frog 

as represented in the margin. The skin being- 
removed, the crural nerves, C D, may then be 
perceived issuing from the spine, A B, and re- 
sembling two white threads ; a silver wire, E, is 
to be passed under the nerves, and a small plate 
of zinc, F, to be laid on the muscles of the thighs ; 
then on bringing the metals into contact, either 
directly, or by a bent silver wire passing from 
one to the other, the limbs will be effected with 
convulsive twitchings, which may be re-excited 

at pleasure for some time, by suspending and renewing the contact 

of the metals. 

71. Similar phenomena may be produced by treating in this 
manner any animals ; but cold-blooded animals, as frogs, toads, 
serpents, and fishes retain their excitability longer than those with 
warm blood, though experiments made with the latter, under 
proper arrangements, have a more imposing appearance. Live ani- 
mals also display signs of sensibility to the influence of galvan- 
ism; and experiments may thus be made with live flounders, 
which may readily be procured in any place near the sea-coast. 
If a flounder be laid in an earthenware plate, on a slip of zinc, 
and a piece of silver or gold placed on its back, on connecting 
the zinc with the other metal, by a bent wire, strong muscular 
contractions will be excited in the fish. 

What phenomena attributable to electric currents excited by metals 
were observed by Sulzer ? 

What was the nature of Galvani's original discovery? 

What was the second point ascertained by his experiments ? 

How may this be exhibited ? 

What classes of animals are best adapted for exhibiting- the effect of 
muscular contraction after death ? 

How may the Galvanic effect be produced in the case of a living animal r 
2 o 2 




438 ELECTRICITY. 

72. In these and nnalagous experiments it is requisite that the 
separate pieces of metal should be of different kinds; and the 
effects are most striking when one metal is readily .soluble in 
acids, as is the case with zinc, and the other difficultly soluble, 
as silver, gold, or platina. Hence two insoluble metals, as gold 
and platina, applied as above directed, have hardly any effect; 
while gold, platina, silver, or copper, may be advantageously op- 
posed to zinc, tin, or iron, to form a galvanic circuit. It musi 
be observed that the effect is chiefly momentary, and the convul- 
sive motions take place at the instant of the contact of the 
metals; but the phenomena may be renewed by separating the 
metals and repeating their contact with each other. 

73. Sulzer's experiment before noticed, may be performed by 
placing a piece of silver, as a half dollar, upon the tongue, and 
a disk of zinc under it, and on bringing together the edges of the 
metals while their flat sides remain in contact with the tongue, 
a peculiar taste will be perceived, and a sensation approaching to 
a slight electric shock, especially if the metallic plates have rather 
extensive surfaces. In that case, also, a flash of light will some- 
times pass before the eyes ; but this latter phenomenon may be 
more certainly excited by placing one of the metals between the 
upper lip and the gums, and the other on the tongue, and bringing 
their edges in contact as before. 

74. It has been found that when two metals are brought into 
contact, and then separated, they will exhibit opposite states 
of electricity. Thus if an insulated disk of zinc be laid on one of 
silver or copper, and then removed by means of some non-conducting 
substance, the zinc, on being applied to a delicate electrometer, 
will show positive, and the silver or copper, on the other hand, 
negative electricity. Whence it may be inferred that a portion of 
free electricity had been developed by the metals, and to the 
passage and reunion of the two opposite kinds are to be attributed 
the convulsions of the muscles of animals when their nerves are 
in contact with them placed in a galvanic circuit. 

75. The effect of the contact of different metals may be exhibit- 
ed by placing on the cap of a gold-leaf electrometer, a large plate 
of any metal, and sifting over it zinc filings through a copper sieve, 
insulated by a glass handle ; when it will be found that the leaves 
will diverge with positive electricity, and the sieve will become 
negatively electrified. On repeating the experiment, but using a 
zinc sieve to sift copper filings, the effect will be reversed, and the 
electrometer will show that the copper filings are negatively elec- 
trified, while the zinc sieve will display positive electricity. 

What characteristic properties of the metals employed, favour the suc- 
cess of this experiment ? 

How may Sulzer's experiment be conveniently repeated ? 

What effect may it produce on the organ of sight ? 

In what states are two metals left after having been in contact with each 
other p 

How are the convulsive motions to be explained ? 

In what other manner may the effect of contact be exhibited ? 



/^ 



GALVANIC CIRCLE. 



439 




76. A simple galvanic circle may be formed, by the apparatus 
represented in the margin, consisting of a plate 

^r% of zinc, Z, and one of copper, C, immersed to a 
certain depth in sulphuric acid greatly diluted 
with water, contained in a glass vessel. Then, 
when the upper edges of the metals are brought 
in contact, a current of electricity will take 
place, the positive electric fluid circulating from 
the zinc to the acid, from the acid to the copper, 
thence again to the zinc, and so on in the direc- 
tion indicated by the darts ; the negative current 
being in the opposite direction. 

77. Various modifications of this arrangement may be contrived: 
thus, instead of making the metals communicate immediately, as 
above, a wire of any metal may be attached to the upper extremi- 
ties of each plate, and when the wires are brought together the 
circuit of electricity will go on, but when they are separated, it 
will be interrupted. By this means the electric currents may be 
directed through any bodies, by placing them between the wires, 
so that they may form a part of the circuit, and various effects may 
be produced. The wire connected with the zinc in this case is 
called " the negative wire," and that connected with the copper 
"the positive wire." By some writers they have been denomi- 
nated positive and negative rheo-phores.* 

78. The effects of such an arrangement as that just described, 
at least with small metal plates, will be but inconsiderable. Hence 
Professor Volta conceived the idea of forming what may be term- 
ed a compound galvanic or voltaic circle, by arranging a number 
of disks of different metals, as zinc and copper, with cloth or 
pasteboard soaked in some acid or saline solution between them ; 
as thus the effect might be indefinitely augmented, according to 
the number and size of the. disks. 

79. The apparatus may be fitted up as represented in the annexed 
figure, consisting of an equal number of silver or copper coins, 
or flat pieces of either metal, and of similar pieces of zinc, ar- 
ranged one above another, with wet pasteboard between them in 
the following order : zinc, copper, wet pasteboard, denoted by the 
letters Z, C, W, in successive layers throughout the series. One 
end of the pile must terminate with a zinc plate, and the other 
with one of copper, with each of which wires may be con- 
nected; and the whole should be made steady by fixing the 

Which electrical state is taken by the copper in a simple galvanic pair 
or circuit? 

In what manner may the effects of such a circuit be displayed ? 

What different names are given to the conductors usually attached to 
the opposite extremities of the galvanic arrangement ? 

In what manner did Volta undertake to augment the power of the gal- 
vanic apparatus ? 

Describe the pile of Volta. 



* Current-bearers, from Vtov, a current, and *o ? sco, to bear. 



440 



ELECTRICITY. 



disks between three vertical glass rods, pro- 
perly varnished, and cemented into two thick 
pieces of wood, one of which serves as the base 
and the other as the cover of the pile. Any 
number of such piles may be united so as to con- 
stitute a Voltaic battery, by making a metallic 
communication between the last plate of one pile 
and the first of another, to any extent. 

80. The Voltaic pile will be found highly ef- 
ficient, and forms a convenient instrument, so 
long as the cloth or pasteboard disks between 
the metals retain their moisture ; but when they 
become dry, the pile is rendered comparatively 
inactive. Volta, therefore, contrived a different 
which has been given the French designation 
Couronne de Tasses, as consisting of any number of glasses partly 
filled with diluted acid, with a plate of zinc and another of cop- 
per in each as before described ; and the zinc plate in one glass 
being connected with the copper one in the next, throughout, 
the circuit might be completed by wires attached to the termi- 
nating plates. 

81. But this instrument, though not liable to the same objection 
with the pile, was inconvenient, and therefore has been super- 
seded by various other arrangements, among which we select for 
description the Galvanic trough, or as it also is termed, the Galvanic 
battery of Mr. Cruicshank. It may consist of a trough, T, con- 
structed of baked mahogany, with partitions of glass in the inte- 
rior; or it may be formed of Wedgwood ware, with interior cells, 




arrangement 




How is the efficiency of the pile limited in regard to the time of its 
action ? 

What other arrangement of the elements was devised by Volta ? 
What is the construction of the couronne de tasses, or " crown of cups?" 
Describe the Galvanic batterv. 



GALVANIC TROUGH. 441 

each trough containing ten or twelve. The metal plates P P 
adapted to them are united by a bar of baked wood A B, so that 
the whole set may be let down into the trough, or lifted out to- 
gether. 

82. The cells are to be filled with water or diluted acid when 
the instrument is to be used, and the plates placed in them, each 
cell will contain a zinc and copper plate, and the circulation of the 
electric fluid will take place throughout the whole, while wires 
proceeding from the last zinc plate on one side, and from the last 
copper plate on the other, any bodies, by being placed between the 
wires, will form a part of the circuit, and be subjected to the action 
of the electric fluid. When the necessary experiments are com- 
pleted, the plates should be lifted out of the trough, that they may 
not be too hastily corroded by the acid. 

83. Several such troughs may be combined like voltaic piles, after 
the manner before stated ; and if very large plates be employed to 
form the battery, its power will be exceedingly increased. One 
was constructed, for the use of the Royal Institution in London, 
consisting of two hundred separate parts, each part composed of 
ten double plates, and every plate containing thirty-two square 
inches. The whole number of double plates amounts to two thou- 
sand, and their entire surface to 128,000 square inches, or 888 
square feet. 

84. Several forms of Galvanic apparatus have been invented 
and applied in the United States, some of which manifest great 
energy, combined with facility in manipulation. Among them, 
those of Dr. Hare, denominated the dejiagrator and the calorimoto r r, 
deserve particular mention. The former is composed of two troughs, 
in one of which the zinc and copper plates are arranged across 
the trough, so that each pair forms, when united, a separate par- 
tition for a cell, and the whole thus adjusted throughout a length 
of ten feet, is to receive the acid liquor when the trough is to be 
put into action. To one edge of this trough is attached another of 
the same length with the plane of its open side or mouth forming 
a right angle with that of the trough which contains the cells. 
This is to receive the acid when the action of the deflagrator is to 
be suspended. These troughs thus united are hung on an axis 
passing longitudinally through the line which unites their edges 
so as to allow the liquor to be, by the quarter of a revolution, 
transferred from one trough to the other. Many of the brilliant 
and important experiments exhibited by Dr. Hare, are shown by 
means of this apparatus. 

With what are the cells to be filled ? 

What advantage attends this apparatus in regard to the corrosion of 
the metals ? 

How may the power of this sort of batteries be augmented ? 

What was the size of that belonging to the Royal Institution ? 

What is the construction of Hare's deflagrator ? 

By what means is the acid brought to act on the metallic plates in this 
apparatus ? 

How are the metals disposed in the calorimotor ? 



442 



ELECTRICITY. 



85. The accompanying figure represents the defiagrator. The two 
troughs containing the plates are seen at A A and A' A'. When 
the open mouths of these two are in a vertical position, as seen 
in the figure, those of the other two, B B and B' B', containing 
the acid liquor, are in a horizontal one ; on raising the handle at 
the right of the figure, so as to give each pair of troughs half a 
revolution, the aid will be decanted from its receptacle, and flow 
into the trough containing the plates. 




THE CALORIMOTOR. 



443 



86. The calorimotor in which a great quantity of heat accompa- 
nied by little electrical tension is produced, consists of such an ar- 
rangement of the elements as to form in fact but one, or at most, two 
pairs of separate plates ; for all the zinc plates in one half of the 
apparatus being connected together constitute but one plate, while all 
the copper ones being united, afford another. The plates are, how- 
ever, arranged in an alternating series, so as to present their surfaces 
to each other without occupying too great a space. 

The accompanying figures represent the arrangement of parts 
in the calorimotor. A and a are the cubical boxes containing the 
one acidulated and the other pure water ; b b b b is the wooden 

c 
is 



^^ 





z Pc 




Tr = 






*l 






c 


c\'z 






frame containing the zinc and copper plates alternating with each 
other, and from £ to \ an inch apart, T T t t are masses of tin 
cast over the protruding edges of the sheets which are to commu- 
nicate with each other . The smaller figure, representing a hori- 
zontal section through the plates, shows the manner in which the 
junction between the several sheets and the tin masses is effected. 
Between the letters z z the zinc only is in contact with the 
masses. Between c c the copper alone touches the tin. At the 
back of the frame ten sheets of copper between c c, and ten sheets 
of zinc between z z are made to communicate by a common mass 
of tin, extending the whole length of the frame between T T ; 
but in front, as shown in the larger figure, there is an interstice 
between the mass of tin connecting the ten copper sheets, and 

What relation has the electric tension in the calorimotor to that of the 
pile or trough ? 

Describe the several parts of the calorimotor. 



444 ELECTRICITY 

that connecting the ten zinc sheets. The screw forceps, //, may 
he seen on each side of this interstice, holding- the wire which is 
to undergo ignition. A wooden partition, p p, separates the two 
sets of plates of which the apparatus is seen to be composed. 
The swivel at S permits the frame to be swung round after being 
taken out of the acid in A and to be lowered into the pure water 
in a ; this is for the purpose of washing off, after an experiment, 
the acid which might otherwise too rapidly corrode the plates. 

88. The inventor regards this as furnishing an extreme case of 
great heating power with low electric intensity, and also as show- 
ing that the quantity of heat evolved in single large pairs is greater, 
but its intensity less than that given out by an equal quantity of 
metallic surface arranged in several successive pairs. 

89. Though the most efficient voltaic circles, whether arranged 
as piles or troughs, are such as consist of plates of different metals 
and layers of fluid matter containing oxygen, as already described, 
yet combinations may be formed of various kinds of matter, be- 
sides, metals and acids, manifesting analogous effects, though, in 
most cases, with far inferior energy. 

90. Dr. Bacoiuo of Milan, constructed a voltaic pile entirely of 
vegetable substances; using disks of red beet root, two inches in 
diameter, and similar disks of walnut-tree, the latter deprived of 
their resinous matter by masceration in a solution of cream of tar- 
tar in distilled vinegar. With such a pile, using a leaf of scurvy 
grass as a conductor, he is stated to have produced contractions of 
the muscles of a dead frog. Other experimentalists have formed 
voltaic piles wholly of animal substances. 

91. MM. Hachette and Desormes composed piles of layers of 
metallic plates separated by masses of common paste made of 
flour and mixed with marine salt (muriate of soda). This, which 
has been improperly called the dry pile, appears to owe its effici- 
ciency to the attraction of moisture from the air by the salt con- 
tained in the layers of paste. Professor Zamboni nf Verona, made 
a pile with disks of paper gilt on one side, and coated on the other 
with layers of black oxide of manganese made into a paste with 
honey. 

92. The most simple arrangement of this kind is that called 
Deluc's electric column, consisting of disks of paper covered with 
gold or silver leaf, and similar disks of laminated 2inc, properly 
arranged. Mr. G. J. Singer constructed an instrument in this 
manner composed of twenty thousand- pair of disks inclosed in a 
tube of glass of suitable diameter, having at each end a brass cap, 
perforated by a screw for the purpose of pressing together the 

What does it demonstrate with respect to the heat furnished hy a single 
pair compared with that given out by the same amount of metal in other 
arrangements ? 

What materials were used by Baconio in the construction of his bat- 
tery ? 

What materials did Hachette and Desormes employ ? 

What were adopted by Zamboni ? what by Deluc ? 

What account is ^iven of Sinsrer's column ? 



• THE VOLTAIC PILE. 445 

disks, a wire being attached to either screw, so that one might lx. 
in contact with the zinc, and that at the other end with the other 
metal. Each extremity or pole of such a column will affect the 
electrometer, and exhibit electrical attractions and repulsions. 

93. If two upright electrical columns be placed near each other 
with their poles in opposite directions, and their upper extremities 
connected, while a small bell is attached to the lower end of each 
column, and a brass ball is suspended between them, it will alter- 
nately strike either bell, and the ringing thus caused may be kept 
up for a great length of time. Sir J. Herschel mentions his having 
seen such an apparatus in the study of Deluc, which had continued 
in action for whole years.* 

94. Some of the remarkable phenomena produced by the agency 
of the electric fluids, through the voltaic pile or battery, have 
been already noticed; and a few additional experiments may be 
adduced which will serve more strikingly to illustrate the mode 
of action of voltaic electricity, and demonstrate its similarity to 
common electricity. 

95. Among the effects of the voltaic pile may be mentioned the 
production of sparks and brilliant flashes of light, the heating and 
fusing of metals, the deflagration of gunpowder and other inflam- 
mable substances, and the decomposition of water, saline compounds 
and metallic oxides. 

96. The most splendid exhibition of light may be obtained by 
fixing pieces of pointed charcoal to the wires connected with the 
opposite poles of a voltaic battery. When the charcoal points are 
brought almost into contact, a vivid light and intense heat will be 
excited ; and on gradually withdrawing the points from each other, 
a continued discharge of electric fire will take place, forming an 
arch of light of the most dazzling brightness. If the wires be in- 
troduced into a tube partially exhausted of air, and the charcoal 
points be made to approach and then recede as before, the effect 
will be heightened, and the arch of light will assume a beautiful 
purple colour. 

97. Wires of metal introduced into the voltaic circuit may be 
raised to a red or white heat; and wires of moderate dimensions, 
composed of the least fusible metals, as platina, speedily become 
melted. The same effect is produced on some of the most refrac- 
tory substances, as quartz, sapphire, magnesia, and lime ; while 
fragments of the plumbago or of the diamond are dissipated, under- 
going a real combustion. 

How may such columns be employed to maintain oscillation ? 

What is related of the durability of the electric effect in such columns ? 

W nat are some of the effects produced by the voltaic pile ? 

How may electrical light be best exhibited by the galvanic apparatus : J 

What peculiar effect is observed when the experiment is made in vacuo ' 

What refractory substances are fused by the battery ? 

* See Discourse on the Study of Natural Philosophy, p. 343. On the 
principle of Heine's column is constructed the electrical clock mentioned 
in the Treatise on Mechanics, No. 256. 



446 ELECTRICITY. 

98. The chemical powers of the voltaic battery have afforded 
the means for some of the most remarkable discoveries of modern 
times, among which it will be sufficient to mention the decomposi 
tion of potash and soda, and the exhibition of their metallic bases, 
by Sir Humphry Davy. But for an account of his researches, and 
of the modes of effecting various other chemical analyses by means 
of voltaic arrangements, we must refer the reader to the treatise on 
Chemistry, in the second part of the Scientific Class Book. 

99. The decomposition of water by the voltaic battery may, 
however, be shortly noticed as one of the most simple yet impor- 
tant processes exhibiting the chemical influence of electricity. If 
two wires of platina connected with the opposite poles of a bat- 
tery be passed through corks into the extremities of a glass tube 
filled with water, on suffering the electric current to traverse the 
fluid between the ends of the wires, it will be decomposed into 
oxygen and hydrogen gases ; and if one of the wires be of iron, 
or any other easily oxidable metal, the oxygen will combine with 
the iron as fast as it is evolved, and the hydrogen only will appear 
in the form of gas. By a proper modification of the apparatus with 
two platina wires, both gases may be separately collected ; and 
on examination it will be found that they are produced exactly in 
the proper proportions to form water. 

100. The spontaneous evolution of electricity observable in some 
animals, and particularly in certain kinds of fishes, has been as- 
cribed to galvanism ; but though the electrical phenomena exhib- 
ited by the torpedo and a few other marine animals, have much 
analogy with the effects of the voltaic pile or battery, the re- 
searches of philosophers have not hitherto enabled us to ascertain 
how far the structure of the electrical fishes may be assimilated 
to the arrangement of bodies in different states of electricity, 
forming the galvanic pile. The production of electric sparks and 
other phenomena of a similar nature lead to the conclusion that 
electrical excitement is a concomitant property of animal life in 
general. 

101. Many instances are recorded of the spontaneous display of 
electric light issuing from the skin of the human body, and the 
production of electricity by friction, as from the back of a cat, is a 
common and well-known phenomenon. Cardan mentions a Car- 
melite friar, from whose hair sparks issued whenever it was stroked 
backwards. Scaliger gives a somewhat similar account of a 

What remarkable discoveries have been effected by its aid ? 

En what arrangement is the decomposition of water effected by galvanic 
electricity ? 

In what proportion are the elements oxygen and hydrogen found to be 
when separately collected ? 

To which class of artificial electrical phenomena does that of electrical 
fishes bear the strongest analogy ? 

What general facts indicate a relation between electricity and the ex- 
istence of animal life ? 

What examples of electrical developement in the human body, and the 
bodies of other animals, have been recorded ? 



ANIMAL ELECTRICITY. 447 

woman at Caumont, whose hair emitted fire when combed in the 
dark. Ezekiel di Castro, an Italian physician, in his treatise " De 
Igne Lambente," relates of Cassandra Buri, a lady of Verona, that 
when she touched her body but lightly with a linen cloth, it gave 
forth sparks in abundance. Scaliger, above quoted, mentions a 
wmite Calabrian horse, whose coat when combed in the dark 
emitted lucid sparks. Various instances of a similar nature are 
recorded by Bartholin, Beccaria, Saussure, and other writers ; and 
those cases of spontaneous combustion which have been related 
by physicians were probably owing- to the evolution of electricity ; 
but of these further notice will be taken in the treatise on Chemis- 
try. 

102. The electrical animals already alluded to display much 
greater powers in the developement of electricity than those ex- 
hibited by human beings; and the production of the electric shock 
appears in these creatures to be dependent on the will, and the 
power of producing it to be bestowed on them in order that they 
may be enabled to defend themselves from their enemies, or to 
take the prey necessary for their subsistence. Among these ani- 
mals the most noted is the torpedo (raia torpedo), the peculiar 
pow r ers of which were known to the ancients, and are mentioned 
by Pliny, Oppian, and other writers. These phenomena have 
also been noticed by Redi, Koemper, and other modern authors ; 
but Dr. Bancroft appears to have first conjectured that the influ- 
ence of the torpedo depended on electricity, and Mr. Walsh made 
some important experiments which served to confirm this conclu- 
sion. The subject has since been more fully investigated by John 
Hunter, Spallanzani, Humboldt, Volta, and other philosophers. 

103. The torpedo is an inhabitant of several different seas, 
being found on the coast of England, in the Mediterranean, and 
in Table Bay, at the Cape of Good Hope. The weight of the 
animal when full grown is about eighteen or twenty pounds. It 
gives a benumbing sensation, like an electric shock, when touched, 
and these effects are renewed by repeated contacts. The shock 
may be conveyed, like common electricity, through an iron rod or 
a wet line, but not through non-conductors. The greatest shock 
the torpedo can give is never felt above the shoulder, and rarely 
above the elbow-joint; its strength depending more on the liveli- 
ness of the animal than upon its size. The electric discharge is 
generally accompanied by an obvious muscular action in the ani- 
mal, with an apparent contraction of the superior surface of the 
electric organs, and by a retraction of the eyes. 

On what does the production of electric shocks in animals appear to 
depend ? For what purpose is it generally employed ? 

What was known to the ancients respecting the powers of the torpedo ? 

By whom was the true nature of those powers first explained.' 1 

In what parts of the "lobe is the torpedo found ? 

How may the benumbing effect of this animal be transmitted to the 
person without an actual contact ? 

On what does the force of the shock depend ? 

By what effort does it appear to be produced ? 



448 ELECTRICITY. 

104. These fish appear to be greatly weakened by the emission 
of electricity, and those that give shocks most readily soon be- 
come exhausted and die. From dissection of the torpedo it is 
found to be provided with peculiar organs, placed on each side of 
the head and gills, and connected with the nervous system. It 
has been ascertained, however, from the researches of M. GeotTroy 
St. Hilaire, that a similar organic structure is found in other ani- 
mals of the raia genus, which nevertheless exhibit no electrical 
power. 

105. The gymnotus electricus or electrical eel, is a fish having 
similar powers with the preceding. It is a native of the inter- 
tropical regions of Africa and America, being frequently found in 
the rivers and lakes of Surinam; and it was first described in 1G77 
by M. Richer, who was sent by the Academy of Sciences of Paris, 
to make philosophical observations at Cayenne. This fish (which 
was dissected by Mr. Hunter), like the torpedo, possesses peculiar 
electric organs, which consist of divisions, formed by thin plates 
or membranes, ranged transversely, so that in the space of one 
inch there were two hundred and forty of these transverse mem- 
branes. These organs are copiously supplied with nerves, and 
their too frequent use occasions debility and death. It seems, 
however, that they are not essential to the existence of these ani- 
mals, which live and thrive after the organs have been removed. 

106. Humboldt, in his "Tableau Physique des Regions Equa- 
toriales," describes a curious method of taking the gymnoti, by 
driving wild horses into a lake which abounds with "those fish. 
Some of these are very large, and capable of giving most power- 
ful shocks, by which some of the horses are paralyzed and drown- 
ed; but the eels, at length, being exhausted by their own efforts, 
are taken without difficulty. This philosopher states, that the 
gymnotus in giving shocks does not make any motion of the 
head, eyes, or fins, like the torpedo. 

107. Three other electrical fishes have been mentioned besides 
the foregoing, namely, the silurus electricus, found in the Nile ; 
the trichiurus Indicus, which inhabits the Indian seas ; and the 
tetraodon electricus, discovered off the island of Joanna. Little 
is known concerning the two latter ; but they all appear to possess 
the same general powers of evolving electricity with those already 
described. 

10S. That the various phenomena of common electricity and 
galvanism, to which may be added those of magnetism, depend 
on the operation of a common cause, may now be regarded as an 

What is the effect of repeated discharges on the fish itself? 

Where is the gymnotus electricus found ? 

What pe mi liar organs has it in common with the torpedo ? 

P»v what nethod are the gymnoti captured ? 

What other fishes hitherto discovered possess the property of giving 
electrical shocks ? 

What remarkahle chemical effects have been produced by the voltaic 
battery ? 



DIFFERENT KINDS OF ELECTRICITY. 449 

established principle of physical science; but the investigations 
which have led to this conclusion are only of recent date, though the 
experiments on which it is founded appear to be perfectly satis- 
factory. 

109. In the progress of his electrical researches, Dr. Faraday 
found it necessary, for their further prosecution, to establish either 
the identity or the distinction of the electricities excited by different 
means; and in a paper of great value, which has been published, 
he has established beyond a doubt the identity of common electri- 
city, voltaic electricity, magnetic electricit}^ thermo-electricity, 
and animal electricity. The phenomena exhibited in these five 
kinds of electricity do not differ in kind, but merely in degree ; 
and in this respect they vary in proportion to the various circum- 
stances of quantity and intensity, which can be at pleasure made 
to change in almost any one of the kinds of electricity, as much 
as it does between one kind and another. 

110. Dr. Faraday was anxious to determine the relation by 
measure of ordinary and voltaic electricity ; and after various ex- 
cellent experiments he found as an approximation, and judging 
from magnetical force only, that two wires, one of platina and one 
of zinc, each 1-18 of an inch in diameter, and placed 5-16 of an inch 
apart, and immersed to the depth of 5-18 of an inch in acid con- 
sisting of a drop of oil of vitriol and four ounces of distilled water, 
at a temperature of about 60°, and connected at the other extremi- 
ties by a copper wire 18 feet long and 1-18 of an inch thick (being 
the wire of the galvanometer coils), yielded as much electricity 
in 8 beats of his watch, or 8-150 of a minute (3.2 sec.) as the 
electrical battery (of 15 jars) charged by thirty turns of a plate 
machine 4 feet in diameter, and in excellent order. The same re- 
sult was found to be true in the case of chemical force.* 

111. It further appeared, from the experiments of Dr. Faraday, 
that a great number of bodies which when solid were incapable 
of conducting electricity of low tension, acquired by liquefaction 
or fusion the power of conducting it in a very high degree. Such 
are water, and several saline and other substances ; but sulphur, 
phosphorus, camphor, spermaceti, sugar, and various other bodies, 
including some salts, acquire no conducting power when melted. 



What have recent investigations proved with regard to the phenomena 
of Electricity, Galvinism, and Magnetism ? 

in what respect did Faraday find the different kinds of electrical action 
to differ ? 

State the relation in point of magnetic, force and of chemical actionhe- 
tween a four feet plate machine and a single Galvanic pair, with the con- 
ditions of the experiment. 

What is the general effect of liquefaction on the conducting power of 
electrics ? 

What bodies remain non-conductors when melted ? 

* Encyclopaedia Britannica, 7th edition, J 834. pp. 574, 575. 
2 i> 3 



450 ELECTRICITY. 



MAGNETISM. 

112. It was loiig since conjectured by some philosophers that a 
connection exists between electricity and magnetism, and that 
electric and magnetic phenomena arise from the same cause. The 
discovery .of the effects of the contact of metals and other vol- 
taic combinations tended greatly to render the analogy more 
striking; but the grand discovery of the power of electric currents 
to induce magnetism was made only in 1819, by Professor Oersted 
of Copenhagen ; and Mr. Faraday has more recently demonstrated 
the similarity of electricity and magnetism, by ascertaining a 
method of eliciting electrical sparks from the magnet. 

113. The power of the natural magnet or loadstone to attract 
iron was known to the ancients, though they did not avail them- 
selves of it for any useful purpose. The loadstone is an ore of 
iron, originally found in the country of Magnesia, in Asia, whence 
it derived its name;* but it is by no means uncommon in various 
parts of the world. The principal varieties are those called by 
mineralogists natural loadstone, earthy loadstone, and magnetic 
iron dre, all which are oxides of iron; and meteoric iron, or those 
masses which appear to have fallen from the atmosphere,! prin- 
cipally composed of metallic iron and nickel, are in general 
found to be strongly magnetic. All these bodies, as well as some 
other iron ores, have long been known to possess the property of 
attracting metallic iron when brought nearly in contact with it. 
The magnetic property is capable of being communicated to steel 
by touching it with a natural magnet ; and in this manner artificial 
magnets are formed for various purposes. When steel is touched 
by a magnet it acquires permanent magnetism ; but soft iron treat- 
ed in the same manner, though it also becomes magnetic, loses its 
virtue as soon as it is. separated from the magnet. 

114. Other metallic bodies besides iron and steel are suscepti- 
ble of magnetism. This is found to be the case with nickel, co- 
balt, and brass; the first mentioned of these metals especially 
being observed sometimes to manifest a high degree of magnetic 
power. Nor is this property confined to metals, for many other 
substances belonging to the mineral kingdom, as the emerald, the 

What conjecture was formerly made respecting; electricity and magne- 
tism ? 

What is meant by loadstone ? Where was it originally discovered ? 

What particular varieties of minerals belong to the magnetic species ? 

In what manner and to what materials may the magnetic property be 
communicated ? 

What difference arises in magnetizing soft iron from that of hard steel r 

What other substances besides steel and iron are susceptible of being 
artificially magnetized ? 

* In the Greek language the loadstone is called Mzywu. 
f See Treatise on Mechanics, No. 88. 



ELECTRO-MAGNETISM. 451 

ruby, the garnet, and some other precious stones are stated by 
Cavallo* to be susceptible of magnetic attraction. More recent 
researches have led to the detection of magnetism in a great va- 
riety of bodies, including glass, chalk, bone, wood, and other kinds 
of animal and vegetable matter. And since it may be concluded 
that magnetic attraction is onl) 7 ' a peculiar mode of action of the 
electric fluid or fluids, there can be no reason to doubt that its in- 
fluence in particular circumstances must be as extensive- as that of 
electricity, and consequently that all kinds of matter are subject 
to it. 

115. The attraction of iron is to be regarded as only one of the 
peculiar effects of magnetism, but there is another which though 
less imposing and obvious, is highly important : namely, the po- 
larity of magnetic bodies, or that tendency they possess, when 
capable of free motion, to assume such a position that one par- 
ticular part, as one extremity of an iron rod suspended horizontal- 
ly, shall be directed towards the northern regions of the earth, and 
the opposite extremity towards the southern regions. On this 
property depends the utility of the mariner's compass, which es- 
sentially consists of a magnetic needle suspended on a pivot, so 
that it may turn horizontally without obstruction. Such a needle, 
if the box containing it be placed on a level surface, will generally 
be observed to vibrate more or less, till it settles in such a direc- 
tion that one of its extremities or poles will point towards the 
north, and the other consequently towards the south. If the po- 
sition of the box be altered or reversed, the needle will always 
turn and vibrate again, till its poles have attained the same direc- 
tions as before. 

110. All magnets and magnetic bars have a north and a south 
pole; and if the north pole of one magnet be presented to the 
south pole of another, attraction takes place between them ; but if 
two north poles or two south poles of different magnets be made 
to approach, they repel each other. If the north pole of a common 
bar magnet be presented to the south pole of the needle of a com- 
pass, the latter will be attracted, and may thus be drawn from 
its proper direction, which it will recover as soon as it is left at 
liberty; and on the contrary, if a similar pole be presented, as the 
north pole of the magnet to the north pole of the needle, the latter 
may be repelled, and thus driven from its true direction, to which 
it will return when the disturbing object is withdrawn. 

What general conclusion follows the researches of recent experiment- 
ers on this subject ? 

What effect besides simple attraction is an attendant of magnetizing ? 

What practical purpose is subserved by this property of magnetized 
bodies P 

Describe the manner in which this is applied. 

How do poles of the same and those of opposite names respectively af- 
fect each other ? 

* See Philos. Trans, for 1780 and 1787; and Cavallo's Treatise on 
Magnetism, 1787, p. 73. 



452 ELECTRICITY. 

117. When a piece of iron not magnetic is brought in contact 
with a common magnet, it will be attracted by either pole; but the 
most powerful attraction takes place when both poles can be ap- 
plied to the surface of the piece of iron at once. It is on this ac- 
v count that artificial magnets are often bent into the form of a horse- 
shoe, the north pole being usually marked by a line or point to 
distinguish it. 

US. Having thus stated the most common phenomena of mag- 
netism, the reader will be prepared to understand the nature of the 
connexion between electricity and magnetism as deduced from the 
researches of Oersted, Ampere, Faraday, and other philososhers. 
It appears that a metallic wire forming a part of a voltaic circuit 
exercises a peculiar attraction towards a magnetic needle. Thus if 
a wire connecting the extremities of a voltaic battery be brought 
over and parallel with a magnetic needle at rest, or with its poles 
properly directed north and south, that end of the needle next to the 
negative pole of the battery will move towards the west, and that 
whether the wire be on one side of the needle or the other, pro- 
vided only that it be parallel with it. 

119. If the connecting wire be lowered on either side of the 
needle, so as to be in the horizontal plane in which the needle 
should move, it will not move in that plane, but will have a ten- 
dency to revolve in a vertical direction, in which, however, it will 
be prevented from moving in consequence of the manner in which 
it is suspended, and the attraction of the earth. When the wire is 
to the east of the needle, the pole nearest to the negative extremi- 
ty of the battery will be elevated, and when it is on the west side 
that pole will be depressed. If the connecting wire be placed be- 
low the plane in which the needle moves, and parallel with it, the 
pole of the needle next to the negative end of the wire will move 
towards the east ; and the attractions and repulsions will be rela- 
tively contrary to those observed in the former case. The con- 
necting wire will be equally efficient whatever be the metal of 
which it is composed ; and even a small tube filled with mercury 
will answer the purpose. The interruption of the circuit by water, 
unless it be carried to a great extent, does not prevent the action 
of the connecting wire; and its influence, like that of common 
magnetism, penetrates all bodies not too thick, whether conductors 
of electricity or non-conductors. 

120. If an unmagnetized steel needle be placed parallel with 
the connecting wire of a voltaic battery, and nearly or quite in 
contact with it, the two sides of the needle become endued with 

Under what circumstances is the most powerful exertion of magnetic 
force displayed f 

What form must be given to the magnet in order to exhibit this ? 

What effect proceeds from placing over a compass needle, and parallel 
with its direction, a wire connecting two poles of a voltaic battery.'' 

In what direction will the two poles of the needle move when the wire 
is on a level with the needle and parallel in direction * 

What change of tendency will arise from carrying the wire below the 
ueedle p 



ELECTRO-MAGNETIC CURRENTS. 453 

opposite kinds of magnetism ; one side being- attracted by the 
north pole of a mag-net, and the other side by the south pole. 
But if the needle be placed at rig-ht angles to the connecting 
wire, it will become permanently magnetic, one of its extremities 
pointing to the north pole and the other to the south, when it is 
suspended and suffered to vibrate undisturbed. 

121. Magnetism may be communicated to steel by means of 
electricity from an electrical machine, evidencing the identity of 
the cause of attraction in the different cases ; but the voltaic 
battery is more conveniently adapted to the purpose of rendering 
steel magnetic. 

122. Among the various arrangements for the superinduction 
of magnetism in steel bars, one of the most efficient and useful is 
by inclosing the bar within the coils of a conducting wire twisted 
into a helix or corkscrew form, by wrapping it round a glass tube. 
It will then in some degree represent a polar magnet, and a bar 
of steel introduced into the central cavity of the helix will speed- 
ily become highly magnetic. The wire should be coated with 
some non-conducting substance, as silk wound round it, as it may 
then be formed into close coils without suffering the electric fluids 
to pass from surface to surface, which would impair its effect. If 
such a helix be so placed that it may move freely, as when made 
to float on a basin of water, it will be attracted and repelled by 
the opposite poles of a common magnet, forming a kind of voltaic 
magnet. M. Ampere describes such an apparatus under the ap- 
pellation of an Electrodynamic Cylinder. 

123. If a magnetic needle be surrounded by coiled wire covered 
with silk, the transmission of a very minute quantity of electri- 
city through the wire will cause the needle to deviate from its 
proper direction. A needle thus prepared, therefore, forms an in- 
strument adapted to indicate trifling degrees of electricity pro- 
duced by the contact of metals, by slight changes of temperature, 
or by any chemical action of one body on another. The magnetic 
needle thus applied has been termed an Electro-magnetic Multi- 
plier. 

124. Professor Henry and Dr. Ten Eyck have availed them- 
selves of the influence of voltaic electricity on iron, under the 
arrangement above described, to form magnets whose powers 
are most extraordinary. Those gentlemen first constructed an 
electro-magnet capable of supporting the weight of about 750 
pounds ; and they have since formed another which will sustain 

Through what substances may the voltaic current be transmitted with- 
out affecting its influence over the magnet ? 

How may magnetism be communicated by the electrical current ? 

Is the magnetizing power limited to electricity from any particular 
source } 

What arrangement gives the greatest facility in producing the magnp 
tism of steel bars ? 

Mow may the voltaic magnet be constructed ? 

What name has Ampere given to that apparatus ? 

How is the electromagnetic multiplier formed r 



454 ELECTRICITY. 

20G3 pounds, or nearly a ton. It consists of a bar of soft iron 
bent into the form of a horseshoe, and " wound with twenty-six 
strands of copper bell-wire, covered with cotton threads, each 
thirty-one feet long- : about eighteen inches, of the ends are left 
projecting;, so that only twenty-eight feet of each actually sur- 
round the iron ; the aggregate length of the coils is therefore 728 
feet.. Each strand is wound on a little less than an inch : in the 
middle of the horseshoe it forms three thicknesses of wire, and 
on the ends, or near the poles, it is wound so as to form six thick- 
nesses." 

125. With a battery of 4.79 square feet, the magnet supported 
the weight already stated, 20G3 pounds. The effects of a larger 
battery were not tried. It induced magnetism in a piece of soft 
iron so powerfully as to raise 155 pounds. When two batteries 
were employed, so that the poles could be rapidly reversed, it was 
observed that while one of the batteries was removed, the arma- 
ture, with the weights suspended from it, amounting to 89 pounds, 
did not fall, though the magnetic influence must for a moment 
have been interrupted. This seemingly surprising phenomenon 
is readily explained by adverting to the obvious consideration, 
that the interruption and renewal of the voltaic circuit, and conse- 
quent magnetic attraction, occupied too short a space of time to 
admit of the armature becoming sufficiently detached from the 
poles of the magnet for it to sink beyond its influence, before the 
circuit was again completed ; whereas, in general, its action ceases 
as soon as the circuit of electricity is entirely broken, affording a 
striking illustration of the nature and causes of magnetism.* 

126. If any further evidence had been requisite to prove the 
analogy between electricity and magnetism, it might be derived 
from the discovery recently made by Mr. Faraday, of the possi- 
bility of eliciting electric sparks from the common magnet. 

127. One arrangement for effecting this, consists of twelve 
sheer-steel plates, connected together, in the form of a horseshoe; 
with a keeper or lifter made of the purest soft iron. Around the 
middle of the keeper is a wooden winder, having about 100 yards 
of common threaded bonnet-wire, the two ends, composed of four 
lengths of the wire twisted together, being carried out with a 
vertical curve of about | of a circle ; one of these twisted ends 
passing beyond each end of the keeper, and resting on the re- 

Wliat extraordinary results have been obtained in the induction of mag- 
netism by voltaic currents? 

What apparent anomaly was observed by Messrs. Henry and Ten Eyck 
after breaking the voltaic circuit? 

How is it to be explained ? 

What discovery illustrates most forcibly the analogy between electri- 
city and magnetism ? 

What form of magnet has been found most convenient for this purpose ? 

Under what arrangement and operation of the apparatus are electric 
sparks elicited by the magnet ? 

* Silliman's American Journal of Science. 



ELECTRO-MAGNETIC PHENOMENA. 455 

speotive poles of the man-net. A small wooden lever is so fixed 
as to admit of the winder and keeper being suddenly separated 
from contact with the magnet, when a beautiful and brilliant 
spark is perceived to issue from that extremity of the wire which 
first becomes separated from the magnet. By means of this elec- 
tro-magnetic spark gunpowder may be inflamed. 

128. Some researches have been made relative to electro-mag- 
netism by Dr. Ritchie, Professor of Natural Philosophy in the 
University of London. One of his experiments was the continued 
rotation of a temporary magnet on its centre by the action of per- 
manent magnets. This effect is produced by suddenly changing 
the poles of the temporary magnet, and thus at the proper mo- 
ment converting attraction into repulsion. The instrument used 
consists of a series of soft iron cylinders, having ribbons, or ra- 
ther bands, of copper surrounding them, in a similar manner as 
in the apparatus for showing the detonation of oxygen and hy- 
drogen gases by the electro-magnetic spark. The cylinders are 
made to revolve rapidly opposite the poles of the permanent mag- 
net, so that before one current of electricity ceases the other com- 
mences its action. By a peculiar arrangement of the apparatus, 
Dr. Ritchie succeeded in obtaining a series of sparks from the 
common magnet, forming a complete circle, appearing in the dark 
like a lucid ring of the finest diamonds.* 

129. The magneto-electrical machine of Mr. J. Saxton, an in- 
genious mechanic of Philadelphia resident in London, has been 
constructed by Mr. I. Lukens of Philadelphia, in a very neat and 
portable form, and serves to demonstrate the nature of the reaction 
between magnets and electrical currents. It consists of a horse- 
shoe magnet capable of supporting about 10 pounds laid horizon- 
tal with the two poles at the same level. Through the bend of 
the magnet and between the two poles passes horizontally a spin- 
dle, carrying at the posterior part, next to the bend, a small 
toothed wheel acted upon by another of larger diameter turned 
by a crank. This spindle also carries at the anterior, and just 
beyond the poles of the magnet, a piece of soft iron bent into the 
form of a horseshoe, the arms of which are at the same distance 
apart as those of the stationary magnet. This is connected to the 
spindle through the intervention of a disk of brass, so that in re- 
volving the soft iron magnetic poles come successively in contact 
with those of the permanent magnet. 

130. The former is thus successively magnetized and neutral- 
ized, each complete revolution performing the operation twice 
over, reducing its tw r o ends to the condition of north and south 
poles alternately. 

What method was employed by Ritchie to produce continued rotation 

of a temporary magnet ? 

In what manner is the electric spark elicited in Saxton's apparatus r" 
What is the succession of magnetic slates in which the keeper is found 

in this apparatus ? 

* New Monthly Magazine for July, IH33, p. .366 



45ft 



ELECTRICITY. 



The means of manifesting these two stales consists of a wound 
copper wire encircling the keeppr, and having its two ends ter- 
minating, the one in a copper disk on the spindle exterior to the 
keeper, and the other in a small cross-head upon the same axis. 
The disk revolves, having a small part of its lower rim immersed 
in mercury. The cross-head alternately dips its two ends into the 
same cup, and at the moment of rising out of it exhibits a bril- 
liant spark. The whole is supported on a neat mahogany frame.* 

131. The accompanying figure represents Mr. Saxton's magneto 
electric machine. 




M is the horseshoe magnet, composed of three flat magnets 
united, and is about 9 or 10 inches long; a is the axis on which 
revolves the keeper K, to which it is connected through the inter- 
vention cf the brass disk d, and at the other end the pinion h set 
in motion by the tooth wheel and winch H. Round the keeper K 
are wound several coils of wire, iv, all terminating in the two se- 
parate polar wires n and p, of which the former is made to pass 
longitudinally through the wooden axis o on a line with o, but 
connected with the keeper by the rectangular piece of brass r, 
and then serves as an attachment for the little cross-head /, while 
the latter passes along the outside of the wooden axis, and joins 
the copper disk c. 

g is a nearly spherical glass cup, 2| inches in diameter, with 
its mouth turned towards the magnet to receive the end of o with 
the copper disk and cross-head. This cup is supported on a stem 
of glass moveable up and down, and capable of being fixed at the 

By what method is the spark made to pass between one part of the ap- 
paratus and the other ? 

* For a description of Saxton's apparatus see Journal of the Franklin 
Institute, vol. xiii. p. 155 ; and for Dr. J. Green's experiments with it, see 
the same volume, p. 269. 



ELECTRO-MAGNETIC APPARATUS. 



457 



required height by the screw s, the lower part of the cup at m con- 
tains mercury ; e is a nut and screw to keep the cup and stand in 
place. 

132. Professor Henry of Princeton, New Jersey, has construct- 
ed an apparatus for exhibiting- in a temporary magnet a recipro- 
cating motion, the soft iron magnet with its coils of wire being 
suspended like the beam of a steam engine, on an axis, and fur- 
nished with projecting wires which dip into mercurial cups con- 
nected with a voltaic battery at each end of the apparatus. The 
wires are so arranged as to change the poles of the soft magnet 
at every alternation in the movement. Each end of the soft iron 
bar, I, plays between the poles of a permanent magnet curved 
into an elliptical form as seen at M M in the figure. 




133. The north poles of the permanent magnets are both up- 
ward, and when the projecting wires at either end dip into the 
cup, the corresponding end of the soft iron becomes a south pole, 
and is repelled by the south pole of the magnet below it, while 
the elevated end being made a north pole is likewise repelled by 
the north pole of the other permanent magnet. These repulsions 
are so vigorous as to raise the wires out of the cups, and the mo- 
mentum given to the bar throws the apparatus beyond the hori- 
zontal position, so that the wires at the opposite end dip into their 
appropriate cups, and the magnetism of the soft iron bar being in- 
stantly reversed, the operation is repeated.* The zinc element of 
each galvanic pair is marked z and the copper c. The poles of 
the two elliptic magnets are indicated by N and S respectively. 
It will be understood that the coil of wire is continuous, and all 

In what manner has an alternating motion been produced by combined 
voltaic and magnetic influence ? 

To what states are the poles of the temporary magnet successively re- 
duced ? 

How is the soft magnet made to raise its connecting wires from the 
mercurial cups in Prof. Henry's apparatus ? 

What is the best form of apparatus for exhibiting vivid galvanic sparks ? 

On what circumstances does its efficacy appear to depend ? 

* See, for a description of this apparatus, Silliman's Amer. Journal 
of Science, vol. xx. p. 342. The above figure was kindly furnished to thf; 
editor by Prof. Henrv. 

2 Q 



458 ELECTRICITY. 

in the same direction, and that one of each pair of projecting 
wires is the immediate prolongation of the helix, while the other, 
a straight line, comes from the opposite end of the bar, being sol- 
dered to the wire which there terminates the coil. The reversing 
of the magnetism will easily be understood from observing that 
each end of the helix, as P P, dips alternately into a cup from the 
copper, and then into one from the zinc element of the galvanic 
pairs G G. This neat and ingenious apparatus will continue in 
action for a long time, limited indeed only by the durability of 
materials in the galvanic circuits, and their power of furnishing 
a supply of electricity. It is far more energetic than Deluc's 
pendulum, or any similar apparatus depending on the action of 
what is called the dry pile. 

134. Professor Henry has also made some interesting obser- 
vations on the power of voltaic conductors to exhibit sparks pro- 
portioned to their lengths, breadths, and relative arrangement of 
parts, from which it appears that a ribbon of copper coiled into 
a spiral* gives a more intense spark than any other arrangement 
yet tried, and that an increase of length and of breadth in the rib- 
bon gives an increase in the effect, but the limits of this increase 
are not yet ascertained. f 

135. The identity of the electric influence under its various 
modifications — whether as arising from the excitement of elec- 
trics on non-conductors by friction, from the contact of bodies in 
different states, the one being positively and the other negatively 
electrified, from the action of heat, from compression ; and in its 
more anomalous forms, as in the production of meteorological 
phenomena, of animal electricity, or of magnetism, from circulat- 
ing currents of the electric fluids — may be regarded as having 
been satisfactorily demonstrated, in consequence of the experi- 
mental researches and important discoveries of modern philoso- 
phers. 

136. Most of the topics of inquiry just mentioned have been 
already noticed in this treatise, the plan of which prevents the 
introduction of more detailed information, for which the reader 
may have recourse to works of greater extent, and to such as 
are exclusively appropriated to the discussion of the branch of 
science now under review. But the peculiar effects of currents of 
electricity on metallic substances, and especially steel, inducing 
magnetic attraction and repulsion, and the application of the mag- 
netic needle to the purposes of navigation, demand some further 
notice, without which this compendium of science would be im- 
perfect. 

137. The general properties of the magnet, whether natural or 
artificial, and the affinity between contrary poles, and antipathy 

What general truth, in regard to the different kinds of electricity, may 
now be considered as demonstrated by modern experiments ? 

* See Treatise on Mechanics, No. 202, note, 
t See Journ. of Franklin Inst., vol. xv. p. 170. 



TERRESTRIAL MAGNETISM. 459 

between those which are similar, as in the case of bodies posi- 
tively and negatively electrified, have been already noticed. Na- 
tural magnets or mineral loadstones, though sometimes possessing 
strong magnetic power, are not in all respects so well adapted for 
practical purposes as bars of steel artificially magnetized ; and 
the latter are therefore used in the construction of the mariner's 
compass, and other instruments. 

138. There are many methods of inducing permanent magnetism 
in steel ; but one of the most simple and effectual consists in pass- 
ing a strong horseshoe magnet over bars previously hardened and 
prepared. " If bar magnets are to be produced, the bars must be / 
laid in a longitudinal direction, on a flat table, with the marked 
end of one bar against the unmarked end of the next ; and if horse- 
shoe magnets are required, the pieces of steel, previously bent into 
their proper form, must be laid with their ends in contact, so as 
to form a figure like this c$d , observing that the marked ends 
come opposite to those which are not marked ; and then, in either 
case, a strong horseshoe magnet is to be passed with moderate 
pressure over the bars, taking care to let the marked end of this 
magnet precede, and its unmarked end follow it, and to move it 
constantly over the steel bars so as to enter or commence the pro- 
cess at a mark, and proceed to an unmarked end, and then enter 
the next bar at at its marked end, and so proceed. 

193. After having so passed over the bars ten or a dozen times 
on each side, and in the same direction, as to the marks, they will 
be converted into tolerably strong and permanent magnets ; but if, 
after having continued the process for some time, the exciting 
magnet is moved but once over the bars in a contrary direction, 
or if its S. pole should be permitted to precede after the N. pole 
has been first used, all the previously excited magnetism will dis- 
appear, and the bars will be found in their original state. This 
seems to show an effect of circulation rather than of any internal 
mechanical arrangement ; and from the circumstance of a stronger 
power in proportion being produced in thin plates of steel than in 
thick ones, and the acquired magnetism being diminished by rust, 
filing, or grinding, it appears that the virtue communicated is more 
external than internal."* 

140. That a suspended magnet will become fixed in such a di- 
rection as if its opposite poles were attracted by certain points of 
the earth, not very distant from the north and south poles respec- 
tively, was known at an early period, but it is somewhat uncertain 

What kinds of magnets are best adapted to the purposes of navigation f 

What is the method of producing bar magnets } 

How are horseshoe magnets placed in order to be magnetized ? 

In what manner may a magnetized bar be neutralized, and its poles re- 
versed ? 

What facts favour the supposition that magnetism is chiefly confined to 
the surface of a bar ? 

* Report of Mr. Millington's Lectures at the Royal Institution in 1818, 
published in Journal of Science, vol. vi. pp. 82, 83. 



460 ELECTRICITY. 

when navigators first availed themselves of this property of the 
magnet, in order to discover the points of the compass in cloudy 
weather, when neither the sun by day nor the stars by night can 
afford them any assistance. Some writers state that Marco Polo, 
the Venitian traveller, about 1260, introduced among the Italians 
the use of the mariner's compass, having learnt it from the Chi- 
nese ; but it is more commonly regarded as the invention of Flavio 
di Gioja, a native of Amalfi, in the kingdom of Naples, who says 
that he used it in the Mediterranean Sea in the thirteenth century. 

141. The compass which was first employed by European sea- 
men, about the period just mentioned, appears to have been a very 
rude instrument, consisting of pieces of the natural loadstone, 
fixed on cork or light wood, so that it might float on the surface 
of water, in a dish on which were marked the cardinal points of 
the compass. At present the mariner's compass is more accu 
rately constructed, under various forms adapted to peculiar pur- 
poses ; but in all cases composed of a small flattened magnetic 
steel wire, or needle, carefully suspended on a pivot in a hori- 
zontal direction, so that it may vibrate and revolve with the least 
possible degree of friction ; and when intended to be used on board 
a ship, it is made to hang in a frame which preserves its horizon- 
tal position independent of the motion of the vessel. A card is 
placed below the magnetic needle, on which are described two 
circles, one divided into 380 degrees, and the other marked with 
the thirty-two points of the compass ; and thus the direction of 
the magnetic poles in any given situation may be ascertained and 
noted. 

142. There are several circumstances which interfere with the 
regular action of the magnetic needle, and to which, therefore, the 
attention of the mariner must be directed in making observations, 
and performing calculations founded on them, so as to obtain ex- 
act information. These are chiefly the "dip" of the magnetic 
needle, its "secular" and " diurnal variation," and that anoma- 
lous variation that long puzzled navigators, but which is now 
supposed to depend on the attraction of the iron used in the con- 
struction of a ship, or any other portions of that metal which it 
may contain, acting on the compass and disturbing its regular 
operation. The dip of the needle is a tendency manifested by 
either pole to lose its balance except near the equator, the north 
pole sinking as if heaviest on the north side of the equator, and 
the south pole on the south side. As it is of importance to the 

To whom has been ascribed the discovery of the directive influence of 
the earth upon suspended magnets ? 

How early was this principle applied by Gioja? 

Of what did the compass then consist ? 

What is the form of the mariner's compass at present used ? 

In what manner is its card divided ? 

How many circumstances interfere with the regular action of the com- 
pass ? 

What is meant by the dip of the needle ? 

How is its amount to be ascertained ? 



VARIATION OF THE COMPASS. 461 

sailor to be able to estimate the extent to which the compass may 
be thus affected in any situation, an instrument is provided for 
the purpose, called a " dipping needle," in which the magnetic 
wire is suspended in a vertical direction. 

143. It has been already observed that the magnetic poles of 
the earth, or those points towards which the poles of a compass 
are directed, do not exactly coincide with the poles on which the 
earth performs its diurnal revolution; and this deviation of the 
magnetic from the true meridian, is termed the variation of the 
compass. It appears to have been first discovered, or rather ac- 
curately observed by Sebastian Cabot, in 1497; and in the seven- 
teenth century, Henry Gellibrand ascertained that the variation 
itself is subject to a secular alteration. Thus when the variation 
was first noticed at London, the needle pointed to the east of the 
true meridian ; in 1657 there was no variation, the needle pointing 
exactly north and south; it then progressively veered westward, 
having, as is supposed, attained its utmost western declination 
about 1818, when it had reached 24 deg. 36 min. W. ; and it now 
appears to be annually verging towards the east. 

144. Hence it seems not only that the earth's poles of revolu- 
tion do not correspond with its magnetic poles, but also that the 
latter are not stationary, the line of no variation, which passed 
through London in 1657, now crossing the continent of North 
America ; to account for which it has been conjectured by some, 
that the north magnetic pole revolves round the north pole of the 
earth in about 644 years, and consequently, in 1979, the line of 
no variation will again cross the island of Great Briain, as it did 
in 1657; for if the period of revolution of the magnetic pole be 
644 years, half that period, 322 + 1657 = 1979 will indicate 
nearly the next return of no variation, while others supposing that 
the earth's magnetism is due to the electric currents excited by 
the heat of the sun, and that these currents produce magnetizing 
effects, the resultants of which are in the points of greatest cold, 
have conceived that it is to these points that the north pole of the 
needle is directed, and that as such points may vary somewhat 
from age to age, the direction of the needle must vary with them. 

154. The diurnal variation of the magnetic needle was first no- 
ticed by Mr. George Graham, who gave an account of his obser- 
vations to the Royal Society in 1722. It amounts to several mi- 
nutes of augmentation or diminution of the secular variation, at 
any given place, in a day ; and it appears to be occasioned by the 
influence of the sun's light or heat, or perhaps by both. Its quan- 

What is meant by the variation of the needle I 

Is the variation constant, when we compare it through long periods of 
time ? 
Who discovered the secular alteration ? 

Give the history of this alteration as observed in Great Britain. 
When was the daily variation discovered ? 
What is its amount ? 
On what does it appear to depend ? 

2 q 2 



*S2 ELECTRICITY. 

tity is likewise affected by the seasons, being more considerable 
during the summer than in the winter. 

146. The" intimate connexion between electricity and magnet- 
ism, evidenced by the very important discoveries recently made, 
affords abundant reasons for believing that the polarity of the 
magnetic needle must be liable to variations, from the influence 
of certain natural phenomena. Thus some observers, and espe- 
cially Captain Franklin, have stated that the action of the needle 
is impeded by Aurora Borealis, the appearance of which seems to 
be dependent on electricity ; and it has long since been remarked 
that atmospheric electricity often powerfully affects the magnet.* 

147. Another curious fact is the induction of magnetism by the 
exposure of a steel wire or needle to the violet ray of the solar 
spectrum. These and other phenomena recently observed cer- 
tainly indicate such a connexion between heat, light, electricity, 
and magnetism, as affords grounds for regarding them as probably 
depending on a common cause; and the very curious discoveries 
which have been already made, and the striking analogies ob- 
served between the operations of nature under different circum- 
stances,furnish abundant inducement to contemporary philosophers, 
and indeed to all who feel an interest in the advancement of sci- 
ence, to pursue the track already opened, with the fair prospect 
that the assiduous inquirer will be amply rewarded for his time 
and attention to these most important topics of investigation. 

What occasional occurrences influence the action of the magnetic 
needle ? 

What relation has been discovered between light and magnetism? 

* "We have instances," says Professor Winkler, " that magnetic nee- 
dles have acquired an inverted direction by the violence of a flash of 
lightning, the north pole coming to be the south." — Elem. of \A r at. Philos , 
vol. i. p. 331. 



Works in the department of Electricity. 

A Popular Treatise on the subject of Electro-magnetism, by 
By Jacob Green. Philadelphia. 

Cumming's Electrodynamics. 

Cambridge Physics, treatise on Electricity, Magnetism, and 
E lectro-magnetism. 

Library of Useful Knowledge, treatises on the same subjects. 

Singer on Electricity, 1 vol. 8vo. 

Priestly on Electricity, 1 vol. 4to. 

Franklin's Philosophical Papers, 1 vol. 8vo. 

Faraday's recent Researches in the Transactions of the Royal 
Society. 

Becquerel, in the Annales de Chimie 

Thompson on Heat and Electricity. 

Berzelius's Chemistry, (Fr.) vol. i. article Electricity. Pari9 
edition 



INDEX. 



Aberration of the fixed stars, p. 343 
Chromatic, . . 393 

Absolute space 15 

Action and reaction equal, . . 22 
irregular in machines, . 104 
Accelerated motion, . . .36 
Achromatic telescopes, . * 392 
Acoustics, general account of, . 231 
books on, . . • 276 
Adjutages increase the flow of 

water, 170 

.Eolian harp, . . . .260 
Aeriform fluids, . . . .15 
how confined, . 16 
dilate equally, . 301 
Aerolites, '. . 51 
Aeronauts, regulate their eleva- 
tion, 37 

Aerostatics. 218 

Aerial images in concave mirrors, 361 

Air, properties of, ... 180 

currents of, produced by fall 

of water, .... 171 
columns of, in tubes, . . 246 
compressibility of, . . 181 
composition of, . .183 
compressed, .... 193 
combines with water, . . 194 
dry, a bad conductor of elec- 
tricity 426 

elasticity of, . . . .185 
expansion of, by heat, . . 292 
gravity of, . . . .182 
gun described, . . . 205 
thermometer, . . . 294 
vessel of a forcing pump, . 218 
weight of, . . 182, 195 

pump, construction of, . . 186 
vacuum in, . . 195 
mode of action in, . 188 

Albinos, 374 

Ampere's electro-magnetic expe- 
riments, 453 

Angles of incidence and reflection, 28 

of friction, . . .111 

of vision, .... 342 

different kinds of, . .10 

Angular velocity, . . .57 

Animal power, .... 115 

structure, . . .80 

Anvil supported on the body, . 25 

Aplanatic lenses, . . 395 



Aqueducts, Roman . . p. 140 

Arc of oscillation, . . .61 

Archimedes' screw, . . .174 

mechanical feats, . 107 

experiments on 

Hiero's crown, . 150 
Area of stability, . . . .64 
Aristotle, error of, 43 

Amott's hydrostatic bed, . . 135 
Artesian wells, .... 144 
Astronomy, more perfect than 

other sciences, . 13 
how far known, . 12 
Atmosphere, height of a uniform, 206 
extent of, . . 207 
density of, by La- 
place, . . .208 
adhesion, produced 
by, . 209 

Atmospheric refraction, . . 365 
Ass, physical power of, . .119 
Attraction of gravitation, . . 36 
electric and magnetic, 12 
capillary, . . .163 
cohesive, in liquids, . 123 
of metals for heat, . 326 
magnetic, . . . 451 
Attwood's machine, . . .51 

Audibility, 236 

Aurora boreal is, effects of, . . 462 

Automaton, 265 

Axis of a lens 368 

Axle and wheel, . . * . .84 

Bacon, Roger's idea of flying, . 224 
formed speaking 

figures, . . 271 
knew the use of 
lenses, . . 408 
Baconio's vegetable electric pile, 444 
Ball cannon, how brought to rest, 19 
ivory, compressed by colli- 
sion, .... 24 
billiard, moved by springs, 33, 100 
of wax, proves force of gravity, 42 
weight of, at the centre of 



the earth, . 


. 45 


t, how stowed, . 


. 181 


e for weighing, . 


. 81 


false, 


. 82 


Danish, . 


. . 82 


hydrostatic, . 


. 162 



463 



464 



INDEX. 



Balloon, why it ascends, 

inflated with hot air, 



p. 37 
. 221 
. 223 
,. 223 



with coal gas, . 
calculations respecting, . 
affords means of deter- 
mining aerial tempe- 
ratures, . . .283 
Bamberg bellows, . . .192 
Barker's mill, .... 176 
Barlow on seasoning timber, . 290 
Barometer invented, . . . 199 
wheel, . . .202 
water, . ■ . .203 
compound, . . 203 

Barton's iris buttons, . . . 403 
Battery, voltaic, . . . 440 

Bed, hydrostatic. . . .135 

Beer, fermenting, effect of . .194 
Bell, diving . . . 227 

Bellows, hydrostatic, . . . 133 

smith's 192 

Bernouilli on human strength, . 116 

Beudant's silk electrical machine, 431 

Bevell'd wheels, . . . .102 

Bianchi's galvanic clock, . .114 

Billiard table, motions on, . . 29 

Biot's experiments on sound, . 240 

on vocal sound, 263 

or repetitions in 

pipes, . . 270 

Birds, wings of, . . . 81 

Black, Dr. on melting ice, . 305 

Blind person restored to sight, 378 

Bladders for swimming, . 158 

air, in fishes, . 159 

Boat moved by oblique force, 35 

rowing of a, . . .79 

flying 224 

Bodies, falling laws of, . 43 

projected upwards, . 52 

elastic and inelastic, . 24 

flones of the ear, .... 232 

Books on acoustics, . . . 276 

mechanics, . . .121 

heat 332 

optics, . . . 417 

electricity, . . . 462 
hydrostatics, . .165 
hydraulics, . . .179 
pneumatics, . . . 230 

Boiler, Perkins' 312 

Bolognian phosphorus, . . 337 
Bossut on flowing liquids and jets, 1 69 
Bottle imps, . . . .191 

Bramah's hydrostatic press, . 134 

Breast wheel 175 

Brewster on double refraction, . 405 
Bridge, iron arched, raised by 

heat 289 

Briot's coining press, . . . 105 
Bouyancy, centre of, . . .161 



Buchanan on human labour, p. 116 
Bucket supported on the edge of 
a table 69 

Caesar, Julius, employed specula, 408 
Cadet de Vaux on preserving 
lamp glasses, .... 290 

Caloric, 278 

engine, .... 323 
Calorimeter, Lavoisier's, . . 304 
Calorimotor, Hare's, . . 441, 443 
Camel, power of the, . . .119 
water, . . . .162 
Camera lucid a, . . . 414 

obscura, . . 373, 414 

Canal locks, .... 146 
Candle may be shot through a 

plank, 23 

Canton on compression of water, 125 
Capacity for heat, . . . 304 
Capillary attraction, . . 163 

Capstan, ... .85 

double, . . 87 

Cargueros, . . . .117 

Catoptrics, 347 

Cataracts, . 145 

Cavendish on the density of the 

globe, 41 

Celsius' Thermometer, . . 295 

Central forces, . . . .56 

Centrifugal forces, . . 56, 57, 58 

Centripetal forces, . . 56, 57 

Centre of action, . . . 72 

gravity, . . 65, 67 

pressure, . . .137 

curvature of mirrors, . 355 

Chantry's observations on hot air, 326 

Change of motion proportionate 

to force, 28 

Chantepleur apparatus, . . 212 
Charles first inflated balloons 

with hydrogen, . . . 221 
Chimborazo, gravitative attrac- 
tion of, 40 

Chladni's experiments on sound, 240 
do. do. 251 
Chromatics defined, . . . 384 
Chain pump, .... 172 
Circle, divisions of, . .9 
Circus, motions in, 34 
Cistern, flowing of water from, . 136 
regulated by a ball-cock, 160 
Circuit, galvanic, . . . 439 
Clock, electrical, . . .114 
Coaches, when liable to be over- 
turned, 68 

Cochlion 174 

Cog, hunting, . . . .101 

Cogs, 87 

Cohesion of liquids, . . 123 

Coining press, . . . .104 



INDEX 



465 



Colour, cause of, . . . p. 402 
Colours, 384 

number of, . . . 385 

breadth of, in the spec- 
trum 390 

of thin plates and rings, . 399 
Columns, electrical, . . . 445 
Combustibles, . . . .287 
Combustion, a source of moving 

power 114 

Components of oblique forces, 31,32 
Compass needles, . . . 460 

variations of the, . . 461 
Composition of forces, frequent, . 33 
Compensation pendulums, . . 103 
Compressibility of air, . . . 181 
Cone, double, to show centres of 

gravity, 67 

Concords in music, . . . 246 
Contracted vein, • 167 

Concert pitch, .... 253 
Conductors of heat, . . . 320 
Convex mirror, . . . 356 

spectacles, . . 410 

Conductors of electricity, . . 426 
Convulsive motions by galvanism, 438 

Cornea, 375 

flattened in aged persons, 409 
Cords, tension of, . . . .88 
Corks, used in swimming, . . 158 
Cordage, stiffness of, . . .108 
Couronne de tasses, . . . 440 
Coulomb on human labour, .116 
Crickets, notes of, 237 

Cruickshank's battery, . . 440 
Curved surfaces, motions on, . 54 
Curvilinear motions, . . .55 
Cuvier's experiments on the voice 

of animals, . . . . 265 
Cycloid, the curve of isochronism, 61 
Cylinder electrical machine, . 430 

Dalton on liquid expansion, . 301 
Daniel on the pyrometer, . . 298 
on quantity of rain fall- 
ing, . . . .142 
Danish balance, . . . .82 
Davy's discoveries by galvanism, 446 
on heating by friction, . 286 
Deflagrator, Hare's, . .441, 442 
Deluc on the maximum density 

of water, 302 

Delisle's thermometer, . . 296 

Density defined 147 

related to temperature, . 302 
Desaguliers on human labour, . 116 
Descent, of bodies from the moon, 46 
Dexterity, feats of, 71 

Diameter, polar, of the earth, . 45 
Dickenson, Captain, use of diving 
bells, 229 



Differential thermometer, . p. 299 
Diminution of objects by distance, 380 

Dioptrics, 362 

Dipping needle, .... 461 
Direction of gravitation, . . 41 
line of, ... 70 
Dispersion of light by lenses, .390 
Discharge of liquids through ori- 
fices, 169 

Distances measured by sound, . 238 

Diving bell, . . . 227,228 

Diving, deep, effect on the ear, 138, 232 

jackets, . . . . 229 

Distillation, 310 

Dogs employed to labour, . 119 

Dollond's achromatic lenses, . 394 
Double refraction, . . 403 

vision, .... 377 
Dragging friction, . . '.110 
Drebbel, inventor of the thermo- 
meter, . . .293 
supposed inventor of 
microscopes, . .411 
Driving wheel, .... 100 
Drum of the ear ruptured by di- 
ving, . . 232 
capable of ten- 
sion, . . 237 
Dromedary, power of, . . . 119 
Drowning, how to prevent, . 157 
Druids, . ., ■■■■-. . .92 
Duhamel on musical glasses, . 251 
Dynamics defined, . . .17 

Ear, musical 242 

Earth's attraction, . . .39 
Earth supposed to be perforated, 46 

Ebullition 309 

in vacuo, . . . 310 

Echo 267,268 

Eckeberg's extraordinary feats, . 25 
Eclipse of the sun, . . . 346 
Ecliptic, obliquity of, causes the 

seasons, . . . . .281 
Efficiency of wheel work, - . 87 
the inclined plane, 92 
the screw and lever, 96 
compound machines, 106 
the hydraulic ram, . 178 

Efficacious rays 396 

Elater noctilucus, . . . 336 
Elasticity common to all matter, . 23 
a measure of gravity, . 42 
of the human body, . 25 
ofsteam, . . . 316 
as a moving power, . 113 

of air 185 

experiments on, . .191 

Electricity, 418 

excited by friction, . 424 
kinds of, . . . 425 



466 



INDEX. 



Electricity, kinds of,all identical, p 
Electrical animals, 
balance, 

chime of bells, . 
dance, 
jar, . .. 
machine, . . 429, 
Electric fluid, . 

positive and nega- 
tive, . 

Electrics 

Electroluminous ether, 
Electromagnetism explained, 
Electromagnetic cylinder, . 
induction, 
Electrometer, . 

Electroscope 

Elements, four, apparatus of, 
Elephants, strength of, 

walk on tight rope, . 
Engine, steam, .... 
fire, . 
caloric, . 
Equator, centrifugal force at, 
Equilibrium in a balance, . 

by cords and pullies, 
Df lamps suspended, 
stable and unstable, 
of floating bodies, . 
Ericsson's caloric engine, . 
Esquimaux use snow; eyes, . 
ventriloquists, . 
Ether, boiling, freezes water, 
luminiferous, . 
electroluminous, 
Eulenstein, improved the Jews'- 

harp, 

Euler on Barker's mill, 
Eustachian tube, .... 
Evans', Oliver, steam-engine, 
Evaporation, rate of, . 

of ice, 
Expansion of bodies, . . 279, 
liquids, . 
in freezing, 
Experiment, its value to physical 
science, 
on composition of 

forces, . 
on bodies falling in 

vacuo, . 
with the air-pump, . 
Extraordinary rainbows, 
Eye, structure of, 

Fahrenheit's thermometer, . 

Faraday, gasses condensed by, . 
magneto-electric sparks, 
on vibrating plates, 

Fata Morgana, .... 

Fat persons float easily, 



.419 
447 

428 
435 
435 
434 
431 
421 

423 

42? 

16 

421 

453 

452 

42S 

42S 

149 

119 

71 

313 

218 

323 

58 

29 

29 

30 

71 

161 

323 

411 

275 

309 

339 

16 

258 
176 
231 

318 

308 
308 
288 
300 
303 

13 

33 



Feather and guinea apparatus p. 38 
Fecundating powders in the air, 220 
Firmus, feats of strength by, . 25 
Figures, geometrical, . . .10 
Fire engine. .... 218 
Fishes, air bladders in, . . 159 
electric, .... 448 
Flea, comparative strength of, .113 
Float boards, direction of, . . 175 
Floating of bodies on water, . 155 
Floatation employed to raise 

weights, 160 

Florence academy, . . . 125 
Flow of water through apertures, 167 
Fluid, electric, .... 421 
aeriform, . . . .15 
imponderable, . . .16 
magnetic, how used, . 16 

viscous, . . . .122 

Fly wheel, 104 

Flying, art of, . . . 220,224 
Foci conjugate, .... 370 
Focus of a mirror, . . . 355 

lens 370 

Forcing pump 217 

Forks, tuning, differ in different 

nations, 254 

Force of traction, . . .118 

or impetus, how estimated, 22 

of gravitation, . . .50 

Forces, parallelogram of, . . 31 

central, . . . .56 

composition of, . . 31 

union of in one line, . 32 

resolution of, . . . 35 

Fordyce on ponderability of heat, 277 

Fountain, Hero's, . . .193 

Fountains, submarine, . . 144 

intermitting, . .214 

Four elements, . . . .149 

Franklin on learning to swim, . 157 

pouring oil on the sea, 171 

electrical kite of, . . 226 

theory of electricity by, 422 

Freezing, artificial mode of, . 306 

French horn, .... 259 

Friction, 20 

action of, . 108, 109,110 
angle of, . . .111 
wheel, .... Ill 
Frogs electrified after death, . 437 
Fruits, shrivelled, expand in va- 
cuo 190 

Fulcrum, 75 

Fusee, 86 

Gamut, musical, .... 246 
Galileo on falling bodies, . . 43 
discovered the law of os- 
cillation, . . .61 
Gasses, specific gravity of, . . 154 



INDEX. 



467 



Gauges, rain, their construction,/?. 142 
Ganpuy, application of siphons, . 214 
Gay, Lussac, balloon ascension, . 222 
Gasses, different kinds of, . . 183 
their power of conducting 
sound, .... 239 
Gattoni abbate, . . . .260 
Galvani's discovery in electricity, 419 

Galvanism, 436 

Geometrical lines, ... 9 

Gilbert, Dr 418 

Giant's harp, .... 260 
Glasses broken by sound, . . 251 
Globular form of liquid masses, . 165 

Glottis, 262 

Glow worm, .... 336 
Goat employed in mechanical la- 
bour, 120 

Gold, globe of, compared to the 

earth, 39 

Gongs used in China, . . . 256 
Governor for machinery, . .105 
Gray's electrical discoveries, . 419 
Gravity, cause of, unknown, . 11 
affects all bodies, . 20, 38 
centre of, 66 

prevents perpetual mo- 
tion, . 20 
a general moving force, . 36 
is in proportion to masses, 39 
gives velocities inversely 

as masses, . . .39 
influence of, by Cavendish, 41 
its direction, . . 41, 42 
force of, increases with 

the height, ... 42 
is inversely as squares of 

distances, . . .44 
counteracted by centri- 
fugal force, . . 59 
determined by pendulums, 63 
of mountains, . . . 40 
experiments 
on, . . 40 
intensity of, at London, . 50 
centres of, how deter- 
mined, . . .67 
acts as a moving power, 113 
specific, . . . 147, 162 
centre of, in liquid 

masses, . . .166 
causes the flow of liquids, 168 
of air, . . . .182 
Grindstones split by centrifugal 

force, 59 

Guinea and feather experiment, . 38 
Guitar, structure and use of, . 255 

Hammer, a mechanical power, . 78 
how driven upon its 
handle, ... 26 



Hammer, water, . p. 130 

Hammering produces heat, . 287 

Handmill, 104 

Hare's litrameter, . . .150 
deflagrator and calorimotor, 441 

Harmonica, 256 

Hawksbee's electrical discoveries, 418 
Hearing trumpet, . . . 275 
Heat, a moving power, . .114 
cause of, ... 277 

sources of, . . . . 280 
sources of, within the earth, 284 
produced by friction, . . 285 
evolved by compression, . 287 

latent, 303 

specific, .... 304 

propagation of, . . . 320 

reflection of, 329 

Hebstock to raise carriages, . 83 

Heights measured by falling 

bodies, . 51 
barometer, 201 

Heliostat 417 

Helix defined, . . . .95 
Hemispheres, Magdeburg, . . 197 
Henry's mode of magnetizing soft 

iron, . . . 454 
vascillating magnet, . 457 
induction of electricity, . 458 
Hero's fountain, .... 193 
Herbert on expansion, . . . 300 
Herschel on solar heat, . . 280 
on thin plates, . . 400 
Hiero's crown, fraud in, detect- 
ed, 150 

High pressure steam-engine, . 317 
Hildreth on the cicadae, . .261 
Hogshead burst by a small tube, 133 
Home, Sir E. on the fly's foot, . 209 
Hollow cylinders, strength of, .113 
Horn, French, .... 257 
Horse power, standard of, . .118 
Horses, strength of, . . .118 
Humours of the eye, . . . 375 
Human body, stability of, . . 70 
Humboldt's description of car- 

gueros 117 

Humboldt on equatorial climates, 282 
Hunter's screw, . . . ,97 

Hunting cog 101 

Huygens' arc of isochronism, . 61 
Hydraulic machines, . . . 172 

ram 177 

Hydraulics, science of, . .166 

books on, . . .179 

Hydrogen applied to aerostation, 221 

Hydrometer, .... 163 

Hydrostatic balance, . . .162 

paradox, . . . 132 

press, . . 134 

Hydrostatics, science of, . . 122 



468 



INDEX. 



tee, effect of, in preventing fric- 
tion, . . . p. 109 
evaporated at low tempera- 
ture 308 

Iceland spar, .... 404 

Images, double by refraction, . 404 

formed by lenses, . . 372 

in a dark room, . . 340 

in plane mirrors, . . 350 

in a concave mirror, . 360 

Impenetrability of air, . . . 180 

Imponderable fluids, . . .16 

Impressions, durability of, . . 381 

Imps, bottle, . . . .191 

Incandescence, . , . 279 

Incidence, angle of, . . 364 

Inclined planes 91 

motions on, . 53 
Induction of electricity, . .427 
Index of refraction, . . . 365 
Inertia, nature of, ... 20 
Incoercible fluids, . .16 

Inflaming point of vapours, . 327 
Ingenhouz, Dr. on conduction of 

heat 321 

Insects, sounds produced by, . 261 
eyes of, . . . . 373 
Insensible spots on the retina, . 383 
Interference of liquid particles, . 167 
Insulation, electrical, . . 427 

Invariable stratum, . . 284 

Invisible lady, .... 271 
Iris buttons, .... 403 
Isochronism of pendulums, . . 61 
Italian musical scale, . . . 248 
Ivory compressed by collision, . 24 

Jacobi, Barbara, ventriloquist, . 274 
Tar, Leyden, ... . 433 
Jew's-harp, 257 

Kaleidoscope, structure of, . . 350 

Kempelen's automaton, . . 265 

Killarney, echo at, 269 

Kite, paper, its mode of action, . 226 

Knife used by druggists, . . 79 

Kratzenstein's vocal tubes, . . 264 

Labyrinth of the ear, . . .231 

Labour, human 116 

Lacerta gecko 209 

Ladder, how raised, . . .80 
Lama, power of, . . . .120 
Lamp glasses, sinumbral, . . 367 

Lapwing, 261 

Laplace on density of air, . . 208 
Latent heat, . . . .306 

Larynx, 262 

Lathe, turning, . . . .80 
Laws of curvilinear motion, . 28 



Laws of falling bodies, . p. 48 

motion, by Attwood, . 52 

Leaden ball equal to the atmos- 



phere, 


. 206 


Leaning towers, . 


. 69 


Lemon squeezers, 


. 79 


Lengths of pendulums, 


. 162—164 


Lenses, burning, . 


. 328 


optical, . 


. 368 


convex, . 


. 369 


concave, . 


. 371 


achromatic, . 


. 394 


Levelling instrument, . 


. 139 


Lever, properties of, . 


. 74 


mode of its action, 


. 75 


theory of, . 


. 76 


orders of, . 


. 78 


progressive, 


. 78 


compound, 


. b\ 


Leyden phial, 


. 432 


Lifting pump, 


. 217 


Light and heat, cause of, unknown, 12 


interrupted by the 


air. . 334 


transmission of, . 


. 335 



velocity of, . 338, 342, 344 
moves in right lines, . . 339 
intensity ofhovv diminishes, 340 
theory of, . . . .386 
Lightning identical with electri- 
city, . . .419 
rods, . . .436 

Liquid substances defined, . . 15 
pressure on container, . 137 
Liquids, properties of, . . 122 

and solids, how different, 123 
form of, in large masses, 124 
weight and pressure of, . 129 
equal pressure of, . .136 
different in density, . 148 
impact of, 172 

conduct heat imperfectly, 322 
produce electricity by 
friction, . . . 425 
Liquors bottled in condensed air, 227 
Litrameter of Dr. Hare, . . 150 
Loadstone, natural, . . . 450 
Locks on canals, . . . 146, 147 
Locusts, .... 
Ludolfs electrical discoveries, 
Lukens' magneto-electric ir 

chine, 

Luminous bodies, 

Luna? bow 

Lyon's account of arctic dogs, 
Lyre, account of the, . 



Machine, Attwood's . 

effects of, how investi- 
gated, 
complex, 



261 
419 

455 
333 
398 
119 
254 

51 

72 
98 



Machine, compound, how esti- 
mated, . . p. 
usefulness of, 
Mainspring of a watch, 

Magic lantern 

Magdeburg hemispheres, . 

Magnetism, 

terrestrial, 
Magnetizing, .... 
Malus discovered polarization, . 
Maskeleyne, experiments of, 
Masses and velocities produce 

momentum 

Mast-head, ball dropped from, . 
Materials used in the arts, . 
Maximum density of water, 
Mechanics, nature of, . 

necessity of, 
Mechanic powers, 
Media, refracting, 
Medium, resistance of, to motion, 
Mechanical use of the gases, 

Melville Island 

Meniscus lens, .... 
Mercurial gauge, 
Metals, polished, bad radiators, . 
Metronome, Maelzell's, 
Micrometer screw, 
Microscope, simple, . 
compound, 
solar, 
lucernal, . 
Middle C of the piano forte, 

Mill, Barker's 

Minerals luminous after heating, 

Mirage, 

artificial, 
Mirror, plane, .... 
concave, effects of, . 
Chinese, . . . 
burning, .... 
Mixtures, calorific, 
frigorific, 
Mobility defined, 

how estimated, 
Moccia's power of floating, 
Molard restoring the position of 

walls, 

Momentum, how estimated, 

of power and resistance, 
Montgolfier's hydraulic ram, 

balloon, . 
Moon seen through clouds, . 

phases of the, . 
Morveau on Wedgewood's pyro- 
meter, 

Motion requires an active cause, . 
affected by inertia, . 
different kinds of, . 
direction of, . 



1NE 


EX. 


4ey 




Motion accelerated, . . p. 36, 47 


105 


on inclined planes, . 


52 


112 


rotatory, . 


99 


86 


conversion of, . 


101 


415 


of liquids, how caused, 


166 


197 


in distant bodies, 


380 


450 


Moving bodies, . . . 


25 


459 


force, oblique, 


35 


459 


powers, . 


113 


406 
41 


Muschenbroek's jar, . 


432 


Nairne's electrical machine, 


429 


21 


Natural philosophy, object of, 


14 


34 


forces producing motion, 
Nature supposed to abhor a va- 


72 


112 




302 


cuum, 


199 


17 


Navigation of rivers, . 


146 


17 


Newcomen's engine, . 


314 


72 


Newton's laws of curvilinear mo- 




364 


tion 


28 


19 


cause of planetary mo- 




184 


tions, 


38 


282 


theory of light, . 


386 


372 


error respecting disper- 




187 


sion, 


393 


331 


experiments on colour- 




65 


ed rings, . 


400 


98 


Niagara, cataract of, . 


145 


411 


Nighthawk, noise of, . 


261 


412 
416 


North pole, weight of a body at 

the, 

Notes, musical 


45 
247 


417 


249 
176 
338 


Nut crackers, .... 


79 


Oblique action, . 


88 


351 


Octave organ pipes, 


244 


352 


Oersted, water compressed by, 


126 


349 


discovers electromagnet- 




359 


ism, 


425 


357 


Oil, effect of, in calming ripples, 


171 


328 


Opaque bodies, . 


407 


288 


Optical axis, 


404 


307 


instruments, . 


407 


18 


Optics, science of, 


333 


18 


works on, . 


417 


156 


Orbits of the eyes, 


375 




Ore, a mode of raising, 


86 


289 


Organ pipes, length of, 


244 


72 


Oscillation of pendulums, . 


59 


, 78 


centre of, . 


64 


177 


Otto Guericke's air-pump, . 


190 


221 


hemispheres, 


198 


18 


Overshot wheel, . 


175 


346 


Oxen, power of, , 


120 


298 


Oxy hydrogen microscope, . 


417 


19 


Pacos, power of, . 


120 


21 


Paganini, .... 


255 


27 


Papin's digester, . 


311 


27 


Parachute, .... 


223 



2R 



470 



INDEX. 



Paradox, hydrostatic, . . p. 132 
Paraselene and Parhelia, . . 353 
Parallelogram of forces, . • 30 
Parallelopiped, sides of, . . 33 
Parallel motion of Watt, . .102 
Pascal, discovery of in hydrosta- 
tics, . . . .134 
on barometric measure- 
ments 201 

experiments on liquid co- 
lumns, .... 204 
Pendulums, oscillation of, . . 60 
weight of, . . 61 
length of, . . 62 

compensating, . . 103 

Penumbra, 345 

Percussion and pressure compa- 
red, 93 

Perkins, steam boiler of, . . 312 

on compressibility, . 126 

on condensation of air, . 180 

Peron on human labour, . .118 

Persian wheel 173 

Phases of the moon, . . . 346 
Phantasmagoria, .... 416 
Phantasmascope, .... 382 
Philosophical inquiry, limits of, . 13 
Philosophy, natural, arrangement 

of, . . 14 
defined, . 1 1 
Phosphorescence of matter, . 335 
of the sea, . 337 
Physical sciences, province of, . 14 
Piezometer of Perkins, . .127 
Pincushion and cannon ball com- 
pared, . . . . . 23 
Pile, electric, . . . 444 

voltaic, .... 439 
Pinion and wheel, . . .99 
Plane, inclined, . . 53, 91, 92 
Plaster of Paris, mirrors made of, 328 
Plates, colours of thin, . .399 

Pliny on speaking nightingales, . 266 
Pluviameter or rain-gauge, . . 142 
Pneumatics, science of, . . 179 
Polarization of light, . . . 406 
Polaritv, magnetic, by light, . 462 

PolyedVons 10 

Pompeii, lead pipes used in, . 140 
Porters, strength of, . . . 117 
Potter's wheel, . . . .59 
Power or impulse defined, . . 21 
when counterbalances re- 
sistance, . . . 105 
Powers, mechanic, division of, 72, 73 
moving, . . . .113 
Press, hydrostatic, . . .134 
Pressure on curved surfaces, . 55 
and percussion, . . 93 
centre of, . . .137 



Pressure, hydrostatic, . . jo. 131 
of air on the body, . 206 
Prince, Dr. improved the air-pump, 196 
Printing press, Russel, . . 88 
Prisms, defined, . . . .11 

refracting, . . . 385 
Proteus, supposed meaning of, . 14 
Pumps 214 

with holes in the suction 
pipes, . . . . 216 

lifting 216 

Pulley described, . . 89, 90 

compound, . . .91 
Pupil of the eye dilated, . .376 
Puy de dome.'experiments on, . 201 
Pyronomics, .... 277 

Rack and pinion, . . .102 

Radiation, . . . .327, 330 
Radius of curvature, . . .57 
Railway planes, .... 
Rain, how retarded, . 

quantity of estimated, 
gauge, .... 
quantity of in different coun 
tries, .... 
Rainbow explained, . 
Rarefaction, degree of, 
Rays, efficacious, . 

refracted by drops, 
Reaumur's thermometer, 
Receiver fixed to air-pump, 
Reciprocating motion, . 
Regulation of machinery, 
Reindeer, labour performed by, . 

Remora, 

Rennie on strength of granite, . 
Reed suspended by hair and 

broken, 

Reflected motion, 
Reflection of sound, . 

of light, 

by thin plates, . 

atmospheric, 

from concave surfaces, 358 

from convex surfaces, 354 
Refraction of light, 

angle of, 

index of, . 

double, 

negative and positive 
Refractive power, 
Refrangibility of colours, . . 388 

Resiliency 24 

Resistance defined, . . 21,72 

as related to power, . 21 
Resinous electricity, . . . 423 
Resonances, .... 253 
Resolution of forces, . . .35 
Resultant of oblique forces, 31 



102, 



92 
141 
141 
142 

143 
. 396 
188—195 
. 396 
. 396 
. 294 
. 197 
101 
103 
120 
210 
112 

26 
28 
266 
348 
401 
351 



363 
364 
365 
403 
405 
391 



INDEX. 



471 



Resultant of three or more forces, 


p. 32 


Soda water, 


. p. 194 


Retina of the eye, 


.341 


Solid bodies, 


. 15 


Ricochet motion on water, . 


128 


figures, 


. 10 


Rider in a circus, 


34 


Solids immersed in fluids, 


. 138 


Rings, coloured of Newton, 


400 


pressed by liquids, 


. 171 


Rigidity of cordage, 


. Ill 


Soniferous undulations, 


. 235 


Ritchie's magneto-electric appa 




Sonorous bodies, . 


. 243 


ratus, .... 


455 


Sound, medium of, 


. 233 


Rockets, sky, 


225 


inaudible in vacuo, 


. 233 


Rolling friction, . 


110 


propagated through solids, 234 


Roman aqueducts, 


140 


vibrations caused by, . 234 


Romans understood hydrostatic 




diminished by distance, . 237 


pressure, .... 


140 


inversely as square of dis- 


Rope pump, 


173 


tance, . 


. 238 


ferry boat, . 


35 


velocity of, 


. 238 


Rowing, labour in, 


117 


conducted by water 


. 239 


Rozier and Romain, . 


222 


transmitted by solids 


. 240 


Rumford 


278 


interference of, 


. 231 


on heating by friction, 


286 


reflection of, . 


. 266 


calorimeter of, 


305 


concentrated by a sail, . 270 


Russel press, 


88 


Space, relative, defined, 


. 15 






Spaces described in falling, 


. 48 


Sadler the aeronaut, . 


222 


as square of velocities, . 50 


Sails set to receive a side wind, 


35 


relative to power and re- 


of a windmill, 


35 


sistance, 


. 106 


Saint Bernard, mount, . 


283 


Sparks from voltaic apparatus, . 445 


Sand on vibrating plates, . 


252 


Speaking trumpet, 


. 272 


Santorio's thermometer, 


293 


Specific gravity, by the siph 


on, . 150 


Sappharina indicator, . 


337 


table of 


. 153 


Saxton's electro-magnet, 


55 


of persons, 


. 155 


Scale of musical composition, 


245 


Specific heat, 


. 304 


diatonic, .... 


246 


Spectacles, . 


. 407 


Scales for weighing, . 


81 


Spectre of the Brocken, 


. 361 


Scoriae float on melted metals, 


158 


Spectrum, solar, . 


. 385 


Scott, (Sir W.), insensible to mu- 




Spina, inventor of spectacles, . 407 


sic, 


242 


Spiral, 


95 


Screw, properties of, . 


94 


Spirit, level, 


. 139 


Hunter's, .... 


97 


Sponge, principle of its action, . 164 


efficiency of, . 


95 


Stable equilibrium, 


. 71 


Sealing-wax, electrical state of, 


424 


Stability, area of, . 


. 70 


Seconds' pendulum, . 


64 


Statics defined, . 


. 17 


Seeds conveyed through the air, 


218 


Statera, Roman, . 


. 82 


Seesaw used as a machine, . 


75 


Steel-yard, . 


. 82 


Shadows, 


345 


Steamboat, iron, . 


. 160 


Sharp castings of iron, 


302 


Steam, temperature of, 


. 311 


Shuekburgh on specific gravity, 


152 


engine of Watt, 


. 312 


Sight, how assisted, 


15 


engine of Evans, 


. 319 


Siphon, invested with mercury 




boilers projected upwards, 225 


and water, . 


149 


Stewart on ventriloquism, . 


. 273 


principle of the, . 


212 


Stockenschneider on heating, . 286 


Wirtemberg, . 


213 


Stonehenge, 


. 92 


Sling, principle of, . . 56. 58 


Strength of materials, . 


. 112 


Smoking through the ears, . 


232 


Strings, musical, . 


. 243 


Smoke ascending in air, 


37 


Sun blind, .... 


. S5 


descend when cooled, . 


37 


the fountain of heat, . 


. 280 


and balloon near each other, 38 


influence of, on climate, . 282 


Smoothness, only apparent, . 


109 


Surfaces, convex motions on 


, . 55 


Snow eyes, used by the Esqui- 




Sultzer's discovery on metallic 


maux, 


411 


eftects 


. 427 


Snow melted by black earth, 


331 


Suspension, points of, . 


. 81 



p. 156 
. 157 

. 187 



472 

Swimming, how learned, 
importance of, 
Syringe, exhausting, . 

Table of falling bodies, . 48,51 

specific gravities, . .153 

Tackle of pullies, . . 91 

Tantalus' cup, .... 213 

Tate liqueur, . . . .212 

Telescopes, achromatic, . . 392 

refracting, . .413 

reflecting, . . 414 

Temperature, . . . .282 

remarkable, . . 285 

Temperatures obtained by Daniel, 299 

scales of, . . 298 

Teneriffe, peak of, 379 

Tension 112 

of cords, . . .88 
Thaumatrope of Dr. Paris, . . 381 

Thermometer 292 

scales, . . .298 
mercurial, . . 297 
differential, . . 299 
Time of falling bodies, . . 48 
related to mechanical ac- 
tion, . . . .107 
Tobacco pipe, experiment with, . 69 
Toggle joint, . . . .88 
Torricelli invented the barome- 
ter 199 

Torricellian tubes, . . . 201 

Tournaments, collision in, . . 23 

Torpedo, explosive, . . . 230 

electric, . . . 448 

Towers, leaning, . . . .69 

Traction, force of, . . .118 

Transmitting motion, . . .87 

Transparent bodies, . . . 333 

Transparency of media, . . 334 

Tread wheel, . . . .86 

Tuba stentoriphonica, . . . 273 

Tubes, safety, Watson's, . .159 

capillary, . . . .164 

long, retard flowing water, 170 

of adjutage, . . .170 

Tunics of the eye, . . . 374 

Tuning forks, .... 254 

Twilight, 366 

Undulations, theory of, . . 338 
Uniformly movingbodies, . . 27 
Unstable equilibrium, . . 71 



TNDEX. 



Vacuum, perfect, unattainable in 

the air-pump, . . 195 

nature's abhorrence of, 199 

Vaporization, .... 307 

Variation of gravity, measured, . 59 

the compass, . .461 



Velocity before and after impact, p. 21 
of moving bodies, . . 25 
measured by time and 

space, . . .26 
degrees of, produced by 

falling, . . . 42 
required to project bo- 
dies to the moon, . 46 
acquired, . . 47, 49 
on inclined planes, . 54 
angular, . . .57 
maximum in a jet of 

water, . . .168 
of light, . . . . 342 
of sound, . . . 238 
Vein contracted in flowing liquids, 167 
Venturi, marsh drained by, . 171 
Vent hole in casks, . . .211 
Vessels, two, encountering, ruin- 
ous to the smaller, . . . 23 
Vibrating figures, . . .68 
Vibrations of musical strings, . 235 
of sonorous bodies, . 243 
numbers of, . . 248 
visibly demonstrated, 250 
of luminiferous ether, 387 
Vision, organs of; ... 373 
at different distances, . 376 
distant, . . . .379 
Voice, human, .... 262 
Volta modified Galvani's theory, 420 
Von Mengen, Baron, a ventrilo- 
quist, 275 

Vowel sounds formed by pipes, . 265 

Walcot, Dr. mimicry by, . . 273 
Walrus, foot of, . . . .210 
Water barometer, . . . 203 

compressibility of, . .124 

compressed by Perkins, . 128 

daily supply of, in London, 140 

collected in basins under 
ground, . 

resistance of, to pressure, 

distilled, weights of, . 

camel, 

discharged from a basin, 

wheels, 

works, air-vessel of, burst 

rising in a pump, 

held in an inverted tumbler, 211 
Watt's jointed bars, . . 102,316 

estimate of horse power, . 118 

steam-engine, , 

sun and planet wheels, . 
Wedge explained, 
Weighing machine, . 
Weight of body carried to the 
moon, .... 
as a moving force, . 



145 
152 
153 
160 
170 
174 
177 
200 



314 

101 

93 

83 

44 
72 



INDEX. 



473 



Weight, of liquids, . ' . p. 129 
diminution of, by immer- 
sion, . 130 
only appa- 
rent, . 132 
of air, . . . 182, 184 
Wedgewood's pyrometer, . , 297 
Wells, Artesian, .... 144 
Wheatstone on sound, . . 258 

Wheel removed from a carriage, 77 
and axle, . . . .83 
work, efficiency of, . . 87 
and pinion, . . .99 
driving, .... 100 

toothed 100 

s-un and planet, . .101 
Persian, .... 173 
overshot and breast, . 175 
barometer, . . . 202 



Wheels, friction, . . . .111 

Whirling table 57 

Whispering gallery, . . . 270 

White's pulley 91 

Wick raises oil by capillarity, . 164 
Wind instruments, . . . 256 
pipe of animals, . . 262 
Wirtemberg siphon, . . . 213 
Wollaston on sounds inaudible, . 237 
Wollaston'sconcavo-convexlenses,410 
Works of reference on mechanics, 121 
hydraulics, 179 
acoustics, . 276 
pyronomics,332 
optics, . 417 
electricity, 463 
hydrosta- 
tics, . 165 
pneumatics,230 



THE END. 



Works Piablislted toy Edward €. Biddle. 



I JOHNSON'S MOFFAT'S NATURAL PHILOSOPHY. — A 
I System oi Natural Philosophy designed for the use oi Schools and Acade- 
i niies, on the basis of Mr. J. M. Moffat, comprising Mechanics, Hydrostatics, 
! Hydraulics, Pneumatics, Acoustics, Pyronomics, Optics, Electricity, Gal- 
| vamsm and Magnetism : With Emendations, Notes, Questions tor Ex- 
' annnaiion, &c. &c. By Prof. W. R. Johnson. 

The title of the above work has been changed from "Scientific Class Book, 
Part I." 

JOHNSON'S MOFFAT'S CHEMISTRY.— An Elementary Trea- 
tise on Chemistry, together with Treatises on Metallurgy, Mineralogy, 
Chrystallography, Geology, Oryctology and Meteorology, designed for 
the use of Schools and Academies; on the basis of Mr. J. M, Moffat: 
With Additions. Emendations, Notes, References, Questions for Ex- 
amination, &c. &c. By Prof; VV. R. Johnson. 

The title of the above work has been changed from "Scientific Class Book, 
Part II." 

The Board of Controllers of the Public Schools of the First School Di^-trict of 
Pennsylvania, at a meeting held March 8, 1812, authorized the introduction into 
the Grammar Schools of the District, of the above works by Prof. Johnson. 

Mr. Edward C. Biddl.e, — Philadelphia, June 22, 1835. 

I have carefully examined your " Scientific Class Book, Part I.," and find it what 
has for some time been much wanted in our academies and high schools. The 
emendations, notes, and additional illustrations, are important, and what might 
be expected from one so perfectly at home, both theoretically and practically, in 
the range of Natural Philosophy/as Mr. Johnson is extensively known to be. The 
list of works for reference will be appreciated by intelligent teachers. I have in- 
troduced it as a Text-Book, and commend it cordially to the notice and examina- 
tion of others. CHARLES HENRY ALDEN, 

Principal of the Philadelphia High School for Young Ladies. 

Mr. Edward C. Biddle, Uh Month. 23d, 1835. 

Sir, — I have examined the first part of the Scientific Class-Book ju?t published 
by you, and cheerfully express my opinion, that, for accuracy and comprehensive- 
ness, this work contains a system of principles and illustrations on the subject on 
which it treats, superior to any book of the same size and price intended for the 
use of schools. 

As this volume is the first of a series on the Mechanical and Physical Sciences, 
the public may confidently expect that the successive parts, when completed, will 
constitute a consistent set of treatises peculiarly adapted to the present wants of 
places of education. JOHN M. KEAGY. 

We cheerfully concur in opinion with the above recommendations. 
JOS. P. ENGLES, WILLIAM MARRIOTT, 

HUGH MORROW, RIAL LAKE, 

WM. A. GARRIGUES, BENJAMIN MAYO, 

M. SOULE, JAMES P. ESPY, 

JACOB PEIRCE, REV. SAML. W. CRAWFORD, A. M., 

BENJAMIN C. TUCKER, Principal of the Acadl. Dept. of the 

T. G. POTTS, Universitv of Pennsylvania. 

WM. CURRAN, THOMAS McADAM, 

S. BICKNELL, CHARLES MEAD, 

D. R. ASHTON, JAS. E. SLACK, 
EL. FOUSE, L. W. BURNET, 
C. FELTT, WM. MANN, A. M. 
THOMAS BALDWIN, CHAS. B. TREGO, 
JOHN STOCKDALE, WM. ROBERTS, 
URIAH KITCHEN, THOS. COLLINS, 
THOMAS H. WILSON, SAML. CLENDENIN, 
SHEPHERD A. REEVES, AUGUSTINE LUDINGTON, 

E. H. HUBBARD, JNO. D. GRISCOM, 
WILLIAM McNAIR, N. DODGE, 
JAMES CROWELL, JOHN IIASLAM. 

J. O'CONNOR, 

Mew York, July. 1835. 
Having examined the First Part of the Scientific Class-Book, we feel justified in 
concurring in the above favourable recommendations. 

EDW. D. BARRY, DAVID SOHUPER, 

J. M. ELY, F. A. STRBETER, 

JOSEPH McKEEN, CHARLES W. NICHOLS, 

JONATHAN B. KIDDER, THOMAS McKEE, 



Woi-Ks Published toy Edwai'd C. Middle. 



PATRICK S. CASSADY, G. I. HOPPER, 

WM. R. ADDINOTON, J. B. PECK, 

RUFUS LOCKWOOD, S. JENNER, 

NORTON THAYER, RICHARD J. SMITH. 
JOHN OAKLEY, 

From Alexander D. Bache, A. M., Professor of Natural Philosophy and Chemistry, 

University of Pennsylvania. 
Mr. Edward C. Biddle, 

Sir,— I have examined, with much pleasure, the first part of the " Scientific 
Class-Book." The additions of the American editor appear to me to have well 
adapted the book for use in schools and academies. Its utility to the general reader 
has no doubt been increased bv the same labours. Very respectfully, yours, 

September 16, 1835. A. D. BACHE. 

From JT. W. Fiske, A. .1/., V. D. M., Professor, Amherst College, Mass. 
Mr. Edward C. Biddle, 

Sir, — The "Scientific Class-Book" appears to me, judging from the portions I 
have yet found time to read, a very excellent work. A vast amount of the most 
interesting and valuable knowledge is brought into a small compass, and is gene- 
rafty presented in a very clear and happy method. I hope it will obtain extensive 
circulation, as I know of nothing better adapted for common instruction in the 
sciences which are treated in the part I have seen. 

Very respectfullv, I am yours, 

September 21, 1S35. N. W. FISKE. 

In the opinion expressed bv Professor Fiske, respecting the "Scientific Class- 
Book, Part I.," I can most cheerfully concur. E. S. SNELL, A. M., 

Professor of Mathematics and Natural Philosophy, in Amherst College, 

Massachusetts. 

From Rev. David R. Austin, A. M., Principal of Monson Academy. 
I fully agree with Professors Fiske and Snell, in regard to the " Scientific Class- 
Book," and shall adopt it in the institution of which I have the charge. 

D. ~R. AUSTIN. 

Professor Johnson has rendered the public an invaluable service in bis " Scien- 
tific Class-Book." It is a treasure of useful knowledge, happily adapted not only 
to the wants of the student, but not less so to the general reader. There is so 
much intrinsic merit in this volume, so much of what every youth of every grade 
in the country should, in some sense, be familiar with, that I am sure it needs only 
to be known to ensure it a wide circulation. Aside from its peculiar merit as a 
class-book for the higher schools, I would say to every young man in the United 
States, about to encase in the business of life, Let the Scientific Class-Book be vour 
constant companion." ' E. H. BURRITT. 

New Britain, Conn., Dec. 7, 1S35. 

From Rev. TV. C. Foicler, A. J!/., C. A. S., Professor Middlebunj College, Vermont. 
The " Scientific Class-Book" is admirably adapted to the use of high schools 
and academies, as an introduction to the principles of physical science. It is neither 
a meagre sketch on the one hand, nor on the other is it overloaded with facts. 
The principles are distinctly announced, and the illustrations and proofs are inte- 
resting and satisfactory. 

From Albert Hopkins, A. M., Professor of Mathematics and Natural Philosophy, Wil- 
liams College. 

A work like the "Scientific Class-Book," edited by Professor Johnson, has been 
for some time called for by an increasing taste for science, and a higher standard 
of popular education. Such works ought to meet the popular demand, and to ele- 
vate still higher the standard of attainment. Both these objects, I think, are ade- 
quatelv secured in the present work. I cheerfully recommend it. 

Williamstoicn, Mass., February 22, 1336. 

From Aaron JV. Skinner, Esq., A.M., Principal of a Select Classical School, Neic Haven, | 
Connecticut. 



After three months" use, I have no hesitation in saying, that I think the " Scien- 
tific Class-Book" the best work with which I am acquainted for popular and prac- i 
tical instruction, when the object is to convey useful and interesting information j 
without mathematical demonstrations. Its arrangement is good, and its plan ex- I 
tensive, embracing almost all the topics of Physical Science. The great number 
of facts, experiments, and illustrations by drawings, &x., render it a highly attrac- 
tive hook to the pupil. I cheerfully recommend it as the best and most complete | 
work T have seen for what >t is intended, viz. "A familiar Introduction »o the! 
Principles of Physical Science." 



Worlts Published by Edward €. Middle, 



From Augustus IV. Smith, A. M., Professor of Natural Philosophy arid Mathematics, 
Wesleyam University, Middletotcn, Conn. 

An examination of the " Scientific Class-Book, Part I ," published by you, has 
left a very favourable impression. Of the excellencies of this work, there is. one 
which establishes its claim to public favour, and will most certainly secure for it a 
speedy triumph over works of similar grade and pretensions. I allude to the in- 
troduction of many scientific facts and principles which have hitherto been buried 
in the voluminous and inaccessible records of learned societies, or are of too recent 
ilevelopement to have been earlier iinbodied in any popular work. It appears to 
me to be one of the very few popular scientific works which are not dignified by 
their title, and one of the still smaller class which possess the merits of a public 
ben .'fact ion. AUGUSTUS W. SMITH. 

March 17, 1835. 

From Isaac Webb, Esq., A. M. 

I full v concur in the opinion of the "Scientific Class-Book, Part I.," as ex- 
pressed' by Professor Smith. ISAAC WEBB. 

Extract from a Report made to the Lyceum of Teachers, of Philadelphia. 
Your Committee are of opinion that the book (Scientific Class-Book) in question 
is, in almost every respect, superior to the books now in use, on the subjects it 
embraces. They submit the following reasons as the ground of their preference : — 
1. The different subjects are presented to the student in such a manner, that, 
without some effort on his part, he cannot understand them ; but with that effort, 
he is richly rewarded with an ample fund of valuable facts, arranged, explained, 
and classed in accordance with the recent improvements in physical science. 2. 
At the foot of each page the editor has introduced a few questions so judiciously, 
as to induce the important habit of attention and reflection, without which, to an- 
swer them would be impossible ; thus affording one of the best tests of the actual 
amount of acquirement which the student has made. 3. The work never seems to 
lose sight of the great importance of making all science subservient to the happi- 
ness of man. This, it appears to your Committee, it has done in a high degree, by 
showing to what a great extent the successful prosecution of the arts depends on 
science. 4. The editor appears to have spared no pains in the effort not only to 
render the work in a high degree instructive, but at the same time to introduce 
such interesting (because practical) illustrations, as to make it a very pleasant 
book for those for whom it was designed. In conclusion, your Committee have 
seldom seen a work, intended for youth, in which there is so little to regret and 
so much to approve, as that submitted as the subject of this report. 

From JV*. Dodge-, A. M., Member of the Examining Committee of the American Associ- 
ation for Supply of Teachers. 
I have examined with as much care as my leisure would permit your " Scientific 
Class-Book, Part II.," and shall introduce it into my seminary as a text-book, for 
the subjects of science which it embraces. I am fully convinced, that the scientific 
course presented in these volumes, is decidedly superior in systematic form, as 
well as compass, to any extant in the English language. N. DODGE, 

Principal of Harmony Hall Female Seminary. 

From Colonel James M. Porter, President of Board of Trustees, Lafayette College, 
Easton, Northampton Co., Pennsylvania. 

In this age, wherein utility is the true test of value of publications, "the Scientific 
Class-Book" must meet with public favour, because it so fully deserves it. I 
would recommend it for use in schools, as admirably adapted for the purpose of 
instructing youth in the principles of the physical sciences ; and master mechanics 
would advance their own interests and promote the knowledge of their appren- 
tices, and consequently the value of their services, by placing the work in their 
hands for perusal ; for "every mechanic art is the reduction to practice of scientific 
principles," and the better the principles are understood, the more perfect will be 
that reduction to practice. J. M. PORTER. 

Easton, Pa., April G, 1836. 

From Mr. Cleanthes Felt, M. A. 
I have carefully examined the second part of "the Scientific Class-Book," and 
it appears to me to deserve the patronage of those concerned in the education of 
youth. It is, indeed, in my opinion, the very book so long needed ; I, therefore, 
cheerfully recommend it to parents, guardians, and teachers throughout the United 
Stales. 

From Charles Henry Mddn\ A. M., Teacher, Philadelphia. 
Ma. Edward C. Biddle, 

The surest test of the excellence of a book, — its extensive adoption and use, — has 
been applied, and successfully, to the "Scientific Class-Pnok, Part I. ;" and the 



Works Published by Edward C. Kiddie. 



success o f "Part II.," which you have just published, is therefore not to be 
doubted. Given to the public under the supervision of the same accredited scholar 
as the former volume ; enriched by additional illustrations ; in many places emend- 
ed, and containing a valuable list of bibliographical notices, it can,' with propriety, 
be commended to the use of schools and academies, as well as to private families, 
as a most valuable manual. The treatise on Chemistry, though necessarily very 
short, embraces a perfect outline of the science, and contains the most recent dis 
coveries. The tracts on Metallurgy, Mineralogy, Chrystallography, Geology, 
Oryctology, and Meteorology, are nowhere more lucidly and attractively explained. 
This volume ought to accompany Part I., wherever that is adopted ; indeed, in 
my opinion, it is more deserving of public favour. 

The style and execution of the "Scientific Class-Book, Part II.," as a produc- 
tion of your press, is highly credita'ule. 

February It), 1830. 

From John M. Keagy, M. D., Professor elect of Dickinson College. 

After an examination of the second volume of the "Scientific Class-Book," I 
feel a pleasure in stating that it fully sustains the character given of the previous 
part, as an excellent compend on the subjects of which it treats. The Chemistry 
and Metallurgy, the Geology, and History of Fossils, and the sketch of Meteor- 
ologv, are particularly clear and comprehensive, to be comprised within the limits 
of a single duodecimo. JNO. M. KEAGY. 

Philadelphia, February 15, 1836. 

From Professor Beck, Rutgers College, New Brunswick, JV. J. 

"The Book of Science," by Mr. J. M. Moffat, which forms the basis of the pre- 
sent volume, (Scientific Class-Book,) has already become extensively and de- 
servedly popular in England. Professor Johnson, the American editor of these 
volumes, has greatly improved them by correcting many of the errors contained in 
the original works, and by the addition of many interesting notes, of a set of ques- 
tions for examination, lists of works for reference, <fec. They are very properly 
styled "A Popular Introduction to the Principles of Physical Science." On each 
of the subjects tieated of, there is an amount of information in these volumes 
which is seldom found in elementary treatises of this description ; while this 
information is set forth in such a manner as peculiarly to engage the attention of 
the pupil. In their composition, the best authorities have been consulted, and 
"due acknowledgments have been made wherever they seemed to be required." 
These works are indeed what they purport to be — Scientific Class-Books ; and Pro- 
fessor Johnson deserves well of the friends of science for the labour which he has 
devoted to the preparing of them for the American public. If the friends of educa- 
tion are really in earnest in the business of improvement, these books will soon 
take the place of those incorrect and defective treatises on the various branches 
of physical science which most unfortunately are now so generally adopted. 

Refuge, near Meehanicsburg, Pa., June 15, 1836. 

Sir, — I have examined your "Scientific Class-Book," Parts I. and II. As the 

f result of my examination, I am happy to state that in these books I found a work 

■ well adapted to, and much wanted in our schools. The editor, Professor Johnson, 

' has evinced a sound judgment in the additions made ; and you, as publishers, have 

iconferred a lasting favour upon the public in givingthis judicious work circulation, 

and I trust it will be generally introduced in all our schools and families. I can 

recommend it as one of the best works extant, on the physical sciences. I shall 

cordially use my influence to give the work an extended introduction into schools, 

lyceums, and families. J. D. RUPP, 

Agent for the Pa. Lyceum. 

From C. II. Anthony, Esq., City Surveyor, (Troy, JV*. T.,) and Lecturer on the Natural 
and Experimental Sciences. 

As a teacher of the Natural and Experimental Sciences, I have often felt the 
need of some works in all respects adapted to the present state of science in this 
country. My beau ideal of such a work is fully realized in the "Scientific Class- 
Book," parts First and Second ; and I have lost no time in introducing them into 
my school. Part First is eicellent; hut Part Second I consider as the best text- 
hook in general science ever published in the English language. 

From Samuel Jones, Ji. M., of Philadelphia. 

I have already -riven the First Part of the " Scientific Class-Book" my approval ; 
and now, after having tested the utility of the Second Part, I am fully prepared to 
endorse the favourable opinion expressed by others of its value. i 



Works Published by Edward C. SMddie. 



AN ETYMOLOGICAL DICTIONARY OF THE ENGLISH 
LANGUAGE, — On a Plan entirely new. By John Oswald, Author of 
the " Etymological Manual of English Language/' and '' Outlines of En- 
glish Grammar." Revised and Improved, and especially adapted to the 
purpose of teaching English Composition in Schools and Academics. By 
J. M. Keagy. 

The Board of Controllers of the Public Schools of the First School District of 
Pennsylvania, at a meeting held March 8, 1842, authorized the introduction of 
Oswald's Etymological Dictionary into the Grammar Schools of the District. 

Mr. Edward C. Biddle, 

Sir,— In republishing " l Oswald's Etymological Dictionary," enriched as it is by 
the sensible and well written " Introduction" of Dr. Keagy, you have done a real 
service to the cause of sound education. It is the best work of the kind (designed 
for schools) that I have yet seen, and it must have an extensive circulation. For 
in every well regulated school taught by competent masters, etymology will form 
a prominent branch of study as long as there is an inseparable connexion between 
clearness of thought and a correct use of language. 

Yours respectfully, C. D. CLEVELAND. 

We fullv concur in the above. 



J. M'INTYRE, 
JAMES B. ESPY, 
JNO. SIMMONS, 
B. W. BLACKWOOD, 
E. II. HUBBARD, 

E. NEVILLE, 

F. M. LUBBREN, 
WM. A. GAKRIGUES, 
WILLIAM MARRIOTT, 
RIAL LAKE, 

THOS. T. ASPELL, 
A. MITCHELL, 
CHARLES MEAD, 
WM. MANN, 
WILLIAM M'NAIR, 
JOHN STEEL, 
BENJAMIN MAYO, 
JOHN HASLAM, 
CHAS. HENRY ALDEN, 
THOMAS EUSTACE, 
W. CURRAN, 
BENJAMIN TUCKER, 
M. L. HURLBUT, 
T. G. POTTS, 
CHARLES ATHERTON, 



SAMUEL CLENDENIN, 

E. FOUSE, 

THOMAS CONARD, 

HENRY BILL, 

THOMAS BALDWIN, 

U. KITCHEN, 

DANIEL MAGINIS, 

JOHN EVANS, 

JOSEPH P. ENGLES, 

J. W. ROBERTS, 

BARTRAM KAIGN, 

JNO. D. GRISCOM, 

RICHARD O. R. LOVETT, 

AUGUSTINE LUDINGTON, 

WM. B. ROSE, 

NICHOLAS DONNELLY, 

C. R. FROST, 

WILLIAM ALEXANDER, A. 31. 

M. SOULE, 

J. KAPP, 

JOHN STOCKDALE, 

REV. SAML. W. CRAWFORD, A. M., 

Principal of the Acadl. Dept. of the 

Universitv of Pennsylvania. 
THOMAS H. WILSON, 



HENRY LONGSTRETH, A. M. THOMAS M'ADAM. 

From Mr. William Russell, A.M., author of an Abridgment of Adams' Latin Grammar, 
Teacher, 8fc. 

Oswald's "Etymological Dictionary," revised by Dr. Keagy, is a work which 
will be found invaluable in all schools in which attention is paid to the systematic 
study of the English language. The plan and arrangement of this manual are such 
as to bring under a single glance the etymology of all cognate terms, in addition to 
that of the particular word which happens to occur in any instance ; and the ex- 
tent to which this classification is carried, enables the student to command a sur- 
vey, as it were, of the capabilities of our language, in the expression of whole 
classes of ideas. Oswald's Etymological Dictionary possesses, in this respect, an 
advantage over other works of its class; as most of these are restricted to a mere 
alphabetic arrangement of words, in consequence of which it, becomes exceed- 
ingly difficult to obtain a complete view of any series of derivations. 

I am happy to have the opportunity of introducing the Dictionary in my school, 
as I shall find it a useful substitute for oral instruction, in parsing lessons, both :n 
Latin and English ; having been accustomed to require a statement of the deriva- 
tion or composition of every word in such lessons before that of its inflection or 
other variations. The use of this work will not, therefore, cause me any extra 
arrangement of classes, while it will be of equal assistance to my pupils and my- 
self. Other teachers may find it convenient to introduce the book in the same or a 
similar way. The merits of the work itself, however, are such as to render It con- 
oucivo, in the highest degree, to all purposes of instruction connected with lan- 
guage ; and I have no doubt that if will he adopted in all srchools in which an RC- 



Works Publislicd by Edward C. Bidillr 



curate knowledge of etymology is deemed important. Dr. Keagy'a preliminary 
essay on tlie farms of thought as giving origin to those of expression* will grenaS 
enhance the value of the work to all teachers who place anv reliance on the phi 
Losophy ofinstruction. WM. RUSSELL, 

No. 92, South 8th street, Philadelphia 






From Prof. ~li> r ines, late of the Central High School, Philadelphia 
From a somewhat critical examination of Oswald's Etymological Die 
tionary, and a somewhat extended observation of its results in various 
classes in which it has been used, I am prepared to express my warm ap-i 
probation of the work, and to recommend its general adoption into our 
schools. It is one of the most intellectual class books I have ever met 
with. The spirit in which it is conceived is altogether opposed to that me- 
chanical system of teaching, which so dwarfs and benumbs the intellectual 
powers, and which has heretofore been the bane and the disgrace of so 
many of our educational establishments. When thoroughly studied under 
the direction of a judicious teacher, it cannot fail of producing very marked 
and very valuable results. The Introduction, by the lamented Dr. Keagy, 
is an admirably conceived and admirably executed paper. 

Philadelphia, July 6,1843. E. C. WINES. 

From Mr. W. G. E. Agnew, Principal of Zane street Public Grammar 
School, Philadelphia. 

" I think there is no work authorized to be used in our public schools, so 
eminently calculated to give a boy a critical knowledge of his own lan- 
guage, and in my opinion there is no school book that I am acquainted 
with, that is so useful ; for without the knowledge imparted by it, no pupil 
can become a successful composer, because he does not fully estimate the 
force of words, unless he perfectly understand their meaning, which he 
cannot do except by examining them radically, and the root is not often 
found in our large lexicons, and scarcely ever, if at all, in our smaller 
school dictionaries. 

"Asa book of reference, I think it ought to be found in the library of 
every literary character in the country." 



From. Charles Henry Alien, A. ./If., Chairman of Examining Committee of the Avierican 
Association for the Supply of Teachers. 

Mr. Edward C. Biddle,— 

I have examined with great interest your " Etymological Dictionary," and I am 
convinced that its use will prove of immense benefit to pupils and students nf every 
age. While its prominent design is to furnish a correct knowledge of our lan- 
guage, it will serve also as a most admirable apparatus for mental discipline. To 
the teacher who is not acquainted with the Latin and Greek languages, this work 
is invaluable ; and even to the classical scholar, the number of derivatives placed 
after the several roots, will suggest shades of signification invaluable to him who 
is desirous of expressing his thoughts in definitive terms. 

Dr. Keagy's Introduction is such as a mind like his might be supposed to pro- 
duce. Successfully devoted to elementary instruction for several years, and hav- 
ing given his attention very much to what may be called the philosophy of educa- 
tion, he has here put together a series of facts, and from them deduced principles 
of primary interest, to all, especially to parents and teachers. The work ought to 
be adopted as a text-book in our high schools, and be possessed and daily used by 
our students in college. 



From J. B. Walker, A. B., Teacher, nf Philadelphia. 

Such a book as "Oswald's Etymological Dictionary of the English Language" 
has long been a desideratum. I am gratified to find that this excellent work, im- 
proved and rendered more practically useful by the labours of Dr. Keagy, has at 
length been given to the public. It is well fitted to exercise the pupil's powers of 
discrimination and judgment, and to aid him in acquiring a thorough knowledge of 
the English language. It commends itself to the consideration and adoption ■ 
teachers. 



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